I'm not sure the DUP has actually said something like that. Channel4 may have misinterpreted the following not-so-recent statement of Paul Girvan, MP for South Antrim and DUP transport spokesperson:
As we leave the European Union, the DUP has been clear that there should be no border erected down the Irish Sea. Instead of placing barriers between parts of the United Kingdom we should be building bridges.
According to the same source, the DUP did have a feasibility study for the bridge across the North Channel in its 2015 general election manifesto. (Which Boris Johnson is now fulfilling, in that respect.)
I read that as the DUP doesn't want an Irish Sea border and they want a bridge (to Scotland), i.e. the bridge is the cherry on the cake, not a mitigating/consolation thingy.
Likewise, Arlene Foster was quoted by the BBC saying
"Whilst some foolishly attempt to use Brexit to build a border between Scotland and Northern Ireland, we are more progressive, we want to build a bridge", she said.
Now, it is possible that Boris Johnson may have obtained some concessions from the DUP in return for his support for the feasibility study for the bridge... but I haven't been able to find any confirmation or details on that. Conceivably, such concessions could be related to Brexit terms, but they could also relate to reopening Stormont, which Johnson is trying to do in order to avoid direct rule in case of a no-deal Brexit.
Since I wrote the above, there have been more contradictory news regarding the DUP [not really] making concessions recently; news of today:
A front page article in Friday’s Times newspaper said the DUP has agreed to shift its red lines on Brexit, saying it could accept Northern Ireland abiding by some European Union rules post-Brexit as part of a new deal to replace the Irish backstop.
The paper claimed the DUP, the biggest party in Northern Ireland, had also privately said it would drop its objection to regulatory checks in the Irish Sea, something it had previously said was unacceptable since it would separate Northern Ireland politically and economically from the mainland.
The Times, citing unidentified sources, wrote that, in return for such concessions, Brussels would abandon its insistence on Northern Ireland remaining in a customs union with the EU.
However, DUP leader Arlene Foster insisted that, as previously indicated, any moves which did make Northern Ireland different from the rest of the UK would be unacceptable to the party.
“UK must leave as one nation. We are keen to see a sensible deal but not one that divides the internal market of the UK,” Mrs Foster tweeted [today].
“We will not support any arrangements that create a barrier to East West trade.”
She added: “Anonymous sources lead to nonsense stories.”
The DUP’s Brexit spokesman, Sammy Wilson, also rejected reports that the party was softening its stance, but said he had detected a different tone in talks between London and Dublin.