What was claimed
The current withdrawal agreement effectively keeps us in the single market and customs union.
The withdrawal agreement doesn’t set out the terms of the UK’s future trading relationship with the EU. That would have to be negotiated after Brexit. If the withdrawal agreement passed but no trade deal was then negotiated, the Irish backstop would kick in—keeping Northern Ireland aligned to some of the rules of the single market, but not the rest of the UK. The UK would be in a customs union.