On your (a), the terms do not ask whether the material I posted would be reasonably believed or that the admins would want to punish it. The terms only ask whether I, the poster, know the material is false or inaccurate. I admit that I know "2+2=5" is both false and inaccurate. So, I have violated the terms. Whether those terms are actually binding or whether the admins will choose to punish me for the violation are separate issues. My argument is that the terms are too restrictive and posting "2+2=5" should not be a violation in the first place.
On your (b), the solution to address falsity is to post a correction. If someone is demonstrably wrong, and refuses to respond to comments or other communications that offer a correction, then they will just look dumb and everyone will judge them accordingly (just as happens in the forums when arguments are made with faulty factual premises). Being wrong on the internet should not, by itself, be a violation of terms of service.
(Even ignoring the "2+2=5" bit, I also definitely violated the copyright term by posting the terms themselves, which I do not own the copyright to. Sure, that posting counts as Fair Use under copyright law, but these terms of use for the private website don't care about Fair Use or any other exceptions to copyright.)
And chaos, reading is for losers. You're better off with your head in the sand...