Since this answer ended up longer than I thought it was going to be... Here's a summary:
Yes, there has been an EU declarative commitment to "no hard border" in Ireland, even in the case of no-deal Brexit. Barnier is among those EU officials who said this.
And yes, that causes a dilemma for the EU, or at least a certain trade-off with the need to uphold the integrity of the single market.
The details of how this tension is going to be solved (in case of no-deal) are largely unknown to the public. This secrecy is a deliberate tactic of the EU.
Something that is publicly stated by the EU is an effort to implement the controls away from the demarcation line.
Speculation informed from EU practices says that likely there will be a gradual phase-in of the checks, depending on both political pressures and the dynamics of facts on the ground (how much smuggling is estimated to happen and by what routes, etc.)
There has been a fair amount of waffling around the "hard border" term on the EU side. There isn't a terribly clear definition of the term, so it can mean different things to different people. What is more important are the current preparations for the Irish border in case of no-deal Brexit. These preparation aren't totally transparent either, but what we know insofar:
The EU announced that it has completed its no-deal Brexit contingency plans — but precise arrangements for the politically sensitive question of the Irish border if the U.K. leaves the bloc without a deal are still yet to be finalized. [...]
Officials noted that people and goods will face longer waiting times when crossing borders if there is no deal. The EU has confirmed that in a no-deal British citizens who are not currently resident in the EU will have their passports stamped and be asked a few questions once entering the EU, just like citizens from other third countries.
But officials indicated that arrangements for the Irish border are still not finalized. This is a fraught issue for the EU because if a hard border can be avoided in a no-deal scenario, it calls into question the need for the controversial Northern Ireland backstop — a key part of the Withdrawal Agreement negotiated with London that many Brexiteers say is preventing them from voting for the deal. [...]
While noting that the U.K. is a co-guarantor of the Good Friday Agreement and would in a no-deal scenario have to respect World Trade Organization rules, the [EU] official said that in a no-deal scenario, both the U.K. and Ireland "will need to take unilateral and temporary measures to protect legitimate trade, consumer, and public health. We would again expect the U.K. to live up to its commitment to avoid a hard border while protecting Ireland's place in the internal market."
Asked about physical infrastructure on the Irish border, the EU official said extra controls will be needed but that "we are working very closely with the Irish authorities, we try and perform the controls away from the border." They did not offer details about how this would be done.
So it looks like the promised "no hard border in Ireland" in case of no-deal, means some kind of "extra controls" away from the actual demarcation line of the border. YMMV how you want to spin that.
More extensively, the EU's Irish dilemma in case of no-deal:
Member states have promised to avoid a hard border even if there’s no deal; they have also promised to uphold the integrity of the single market and customs union. [...]
"Where will the controls be?" said a senior EU official in response to questions at a briefing on Monday. "The controls will have to be done where they belong. But that does not mean that we would want to see physical infrastructure at the border. We are working very closely with the Irish authorities to try and perform controls away from the border, if at all possible."
While the speaking points were cleared with Irish officials in advance, that was probably as far as the EU had gone to date in publicly stating that controls would have to happen on the island of Ireland, or, depending on the UK’s post-exit co-operation, along the Irish Sea.
In Strasbourg the EU’s chief negotiator Michel Barnier said that in the event of no deal "there will be no hard border…" but that "there are going to have to be checks carried out somewhere."
Barely had Michel Barnier spoken than Brexiteers seized on his remarks. The campaign group Leave.eu tweeted: "Michel Barnier has confirmed that there would be no hard border in Ireland under a no-deal Brexit - destroying the case for the backstop, and destroying the case against a clean WTO Brexit. Will Remoaners apologise for their nasty Irish border fibs?!"
In the Dáil, the Taoiseach was forced to clarify that when he mentioned "special arrangements" in a no-deal situation, he was not talking about using technology at the border, but about the UK waiving tariffs on goods coming into the North, but not coming into Great Britain.
"Let there be no doubt in this House or in Westminster that when I talk about special arrangements I mean treating Northern Ireland differently from the rest of the UK. It is the UK government's proposal to do exactly that."
So yes, both the hard Brexit camp and the Irish government are trying to spin these (not fully specified) "special arrangements" as to vindicate their point of view. Brexiteers see this as evidence that there will be "no hard border" in Ireland. Taoiseach sees it evidence that the UK will put a border of sorts in the Irish Sea between the rest of UK and Northern Ireland, i.e. vindicating/implementing a kind of backstop anyway. The spin game is on.
As for the checks...
Senior officials say that if there is a hard Brexit on 12 April, it will be impossible both logistically and politically to bring the full gamut of EU internal market and customs union rules to bear in Ireland the next morning.
This will be a managed process driven on the one hand by politics – ie, the promise to avoid a hard border; and on the other hand by risk – ie, how far the EU is prepared to bend the rules to abide by that promise without fundamentally compromising the safety of EU consumers. [...]
"It’s really a question of how much risk we or the EU are willing to accept," says a senior Revenue figure. "It’s a political decision. That’s what it comes down to. If there’s an overriding political decision that a certain level of risk is a cost that must be borne, then that changes all the rules. The political decision determines the administrative practice."
However, that will not mean the EU turning a blind eye, or tolerating a wild west situation. There are countries on the periphery of the EU who will be watching with interest as to what happens on the Irish border.
"The precedent value or risk of anything like this is not to be underestimated," says the official. "The EU is an institution of rules, so precedents are something that have to be weighed up carefully."
The second principle is that so long as the politics of Westminster are live, nothing will be decided that might leach into that debate.
In other words, officials in Dublin and Brussels are extremely sensitive to the risks that any theorising on how to avoid a hard border might, as one official puts it, "pollute" the debate in Westminster.
So that's why the public doesn't find out more about the "special arrangements" until there really is a no-deal Brexit. Or even most of the bureaucracy:
At a very senior level both in Brussels and Dublin the contours of a response will have been set so that the implementation of the plan will happen incrementally, with the technical staff – the "worker bees", as one official puts it – only getting their orders after no deal has happened.
But informed speculation is that such arrangements will be gradually phased in, depending on both political pressures and details on the ground:
A third principle is that while Ireland will be determined, indeed legally obliged, to uphold EU rules, they will be applied incrementally.
Officials have not discounted a scheduling sequence where rules are phased in over time. This is not surprising; if a member state is currently in breach of EU’s rules they are not immediately hauled before the European Court of Justice. The European Commission instead goes through an iterative process of letters, reminders, and warnings. If the member state makes a commitment to become compliant then Brussels waits for them to do it. "It’s not the ideal situation but this is how it’s done in practice," says one source.
A fourth principle is that data and risk will play a major role. In other words, Dublin and Brussels will use data to build up a comprehensive picture of what crosses the border, who are the large operators, who are the small ones, what are they transporting, where is it coming from, and where is it going to. That data will determine what the likely risk is, and that risk will determine what the likely controls are.
"In any customs system it’s a risk based business," says one senior Irish official close to the discussions. "You base your risk on the information available to you. It’s the quality of the information you have which determines how much controlling you have to do.If you have really good information then a tiny amount needs to be checked, because there’s really good confidence about what’s coming in."
And when I'm talking about waffling over the label... here's an example from older news:
Jan 23, 2019:
Ireland will not accept a hard border after Brexit under any circumstances, Taoiseach Leo Varadkar and Tánaiste Simon Coveney have insisted.
Their comments came after a spokesman for the European Commission yesterday suggested a hard border in Ireland would be necessary if the UK left the EU without a deal.
“So what we’re saying is very clear: the Irish Government will not support the re-emergence of border infrastructure on this island,” Mr Coveney told reporters in response to the intervention in Brussels.
Jan 26, 2019
Leo Varadkar said that at the moment the frontier between the Republic and Northern Ireland was "totally open", but "if things go very wrong it will look like 20 years ago".
When asked to detail what a hard border would look like, he told Bloomberg: "It would involve customs posts, it would involve people in uniform and it may involve the need, for example, for cameras, physical infrastructure, possibly a police presence or army presence to back it up.
"The problem with that in the context of Irish politics and history is that those things become targets, and we've already had a certain degree of violence in the last few weeks."
An Irish government spokesman said in a statement after the interview that Mr Varadkar was not referring to the Irish army. [...]
European Commission spokesman Margaritis Schinas told a news briefing in Brussels on Tuesday: "If you would like to push me and speculate on what might happen in a no-deal scenario in Ireland, I think it's pretty obvious - you will have a hard border.
"And our commitment to the Good Friday Agreement and everything that we have been doing for years with our tools, instruments and programmes will have to take, inevitably, into account this fact."