I agree that it isn’t as easily verifiable that it is privacy-respecting without the source code but that’s a couple steps from saying that it is “a falsehood” to say it is.

What made me wonder about it is that this is very specific wording that indicates that they proactively know the author is lying, when it would be very easy to instead say something along the lines of what you said, that it is too hard to verify without access to the source code.

I agree that the language used wasn’t perfect, but… If a claim is not verifiable, it can only be taken on faith. Same as all the existing apps in the category that this one aims to replace. Is there a better word we can use to describe this sort of situation?

I can’t think of one specific word to swap out for “falsehood,” it would be better to just replace the whole phrase. Various things have been bounced around here in the discussion. I’d go with something like “without the source code, unfortunately that can’t be verified.” This is a better phrase all around. It describes the actual problem. And it isn’t unnecessarily accusatory.