As with many things you conflate "There's a ton of info that would suggest that this is false" with "This is false". They're not the same thing, and I know it's not popular to point that out.
At the risk of confusing myself and talking out of my ass (and/or going off-topic), I'm not sure if we can always, or even most of the time, prove something 100%, positively, absolutely true or false in all cases. What I think we can do is look at the evidence and make enough safe assumptions about our hypotheses so they're as good as
absolutely true or false. If I walk out of my bedroom window, I suppose there's some chance, however microscopic, that I will float in the air rather than fall to the ground. But there's no sense in betting on it.
Which isn't to say this current situation is nearly as cut and dry, but if you must have a belief proven absolutely, positively, 100% true or false in all cases, you may be disappointed.
Given my bare minimum knowledge of the subject I just talked about, it's entirely possible I'm completely wrong. If someone with more experience can back me up or set me straight, I'd appreciate it.