If they are not false, you cannot simply claim that, since the proof is insufficient, it is false.

Um, yes you can, or you end up being stuck believing any random "insufficient disproof" hypothesis. I'll name a few, if you want: there's an invisible intangible unicorn in your room, your boss is being mind-controlled by space aliens through subspace, and your door is wired to explode but only when you would be in a position to be killed by it.

If you give any of these meaningful credence - even enough to be "agnostic" about it - then you shouldn't ever use that door, might consider quitting your job, and will work under the assumption that you never have privacy

And no, I don't think I'm that close to infallible, I think I'd have to be that close to infallible to believe something that ridiculous.