Poor analogy here, but if someone tells a police officer that they murdered someone 20 years ago, odds are that person will be arrested and punished accordingly.
I'm sure the cops would at least ask the man who he murdered, that way they can check their files and see if that person existed and indeed got murdered. If not, then he's just a loony toon and/or someone seeking attention. Needless to say the police officers would then proceed to take an official statement, admission of guilt, etc. Similarly, you don't get arrested in Russia for a minor infraction you committed in Mexico. Same goes for crpg - the mod and the forums have always been two separate entities, and the punishment very rarely, if ever would cross over. Infinitely more in-game bans have been handed out than forum bans.
Sure, as you pointed out, the analogy doesn't hold up 1:1, but we should at least have stricter regulations around here other than "he said something, let's believe it and punish him accordingly." Think about it, if I said "Professor sold looms back in the day," would the other devs instantly ban you? Unlikely, they would instead ask for proof first. Same standards apply with an admission of guilt, especially since no one tried so hard as to ask "wait, seriously?" to get confirmation one way or the other.
Edit: Similarly, Havelle got banned only because he "spread lies and slander" about good ole James here. Sorry, but that has never been a ban-worthy offense on the forums, especially if you only made one post about it. If you spam it in every thread, well that can understandably lead to a mute, then a longer mute, and eventually perhaps a ban, yes. But one post saying "i have the dirt on him, lel" is a far cry from a permaban.