I just dunno if I see it as a "false" claim, as much as a claim that's very mildly annoying.
Like, don't think I'm unsympathetic. I remember seeing claims of compatibility in games/books in the '90s and '00s that required serious work to make function together at all, and it used to really irk me when stuff was claimed as compatible but wasn't immediately usable. Eventually I'd seen enough that I could see compatibility was always a spectrum, even between very close games (like CoC editions), sometimes there was something annoying to address.
And I do think WotC's flat statements about it being "compatible" are a little bit cheap and lacking in nuance. Especially as they haven't even finished designing it! I get that the aim was to calm the horses and to encourage people to see where the game is compatible, but I feel like it could have been better handled and they could and should have used more qualifiers.
But at the same time, I think the actual amount of work required to make them work together is going to be fairly low, at least based on the current design of 1D&D (as far as we know it). Especially if you're willing to accept some amount of imperfect-ness, which I think one should be.