Is it true to say that this means the UK will then be unable to permit the import of goods that do not meet EU regulations?
No, that is not true. The Chequers plan was designed to leave the UK with all the freedoms regarding the trade with the UK and the rest of the world while at the same time keeping the UK and the EU in a free trade zone on goods only. The means to achieve this were a common rule-book restricted to rules that enable friction-less transport of goods over the UK-EU border as well as a facilitated customs arrangement, i.e. the UK collecting customs for all goods going into the EU from it (and coming from outside the UK). See sections 1.1 and 1.2 of the white paper.
Within this plan, the UK would have been able to import anything from anywhere, as long as it can make sure somehow that this anything doesn't end up in the EU without complying to EU rules. In practice, this may have proven difficult and it's difficult to estimate how much this would have limited the UK in practice or how much it would have undermined the effectiveness of the EU rules. However, the Chequers plan was definitely not a customs union with the EU.
To make an example: The UK could import chlorinated chicken from the US, under the Chequers plan, if it wanted to. It would then consistently control that this chlorinated chicken does not get transported into the EU or any products made of it (I guess) while at the same time not doing any controls at the UK-EU border directly. The plan did not specify how exactly this would be achieved.
Some relevant quotes from it:
1 Following the decision of the people of the UK in the referendum, the UK is leaving
the EU, and as a result will leave the Single Market and the Customs Union..
3 At the core of the UK’s proposal is the establishment by the UK and the EU of a free
trade area for goods.
7 a) establish a new free trade area and maintain a common rulebook for goods,
including agri-food, covering only those rules necessary to provide for frictionless
trade at the border. ...
7 h) be consistent with the UK’s ambitions as a global trading nation, with its own
independent trade policy..
11 The UK and the EU would maintain a common rulebook for goods including agri
-food, with the UK making an upfront choice to commit by treaty to ongoing harmonisation with EU rules on goods, covering only those necessary to provide for frictionless trade at the border.
12 .. the phased introduction of a new Facilitated Customs Arrangement that would
remove the need for customs checks and controls between the UK and the EU as if in a combined customs territory, while enabling the UK to control tariffs for its own trade with the rest of the world and ensure businesses pay the right tariff
14 ..the UK would apply the EU’s tariffs and trade policy for goods intended for the EU. The UK would also apply its own tariffs and trade policy for goods intended for consumption in the UK. ..