It isn't false, it's a DOJ opinion. The option says that to initiate an impeachment inquiry the House must vote and otherwise it's invalid. They didn't. The President can deny subpoenas based on this opinion.
But that opinion is wrong; like Engel's opinion on McGahn's immunity from having to testify to Congress, and Engel's opinion on not sending the Trump-Ukraine extortion whistleblower complaint to Congress, and pretty much every other legal opinion Engel wrote because his job was to come up with bullshit legal justifications for whatever the Trump Admin wanted.
They won't use his opinion because they don't support it, agree with it, or think it'll stand up to any judicial scrutiny. And they sure don't want to set the expectation that they're going to bind themselves to the legal opinions Trump's cavalcade of clown lawyers pulled out of their asses.
DOJ opinions are valid until a new one is written or it's rescinded. Even if it's wrong, it's valid and can be cited in legal documents. Remember the opinion that said you can't indict a President in office?