You said that the key issue was whether there was a rational basis for the feelings. I agree with you that we can't force people to have different feelings than the ones they have. But our reaction to those feelings can vary based on the reasonableness of the feelings.
I don't think fubarobfusco's claim is that claimed offense ends the discussion in favor of the claimant. Although you correctly note that false claims are cheap, the proper use is intended to begin a discussion about the proper reaction - and the proper reaction might be to do nothing.
Put slightly differently, Bob claiming to be offended by some statement is slight evidence in favor of the hypothesis that the statement caused him harm, of a kind that should not be allowed. Talk is cheap, so the evidence can easily be overcome by contrary evidence. But your position appears to be that Bob's statement is no evidence at all.
I'd like to put in another good word for my second link. It's a five minute video, made by someone far more moderate than you or I. I think it is a reasonable description of the outside view of the archetypal dispute of which this exchange is but one of many examples. If you are really pressed for time, skip to about two minutes in.
I don't think fubarobfusco's claim is that claimed offense ends the discussion in favor of the claimant.
In that case I recommend you reread fubarobfusco's post. His whole point is that if someone objects to the offense claim that means the person doing the objecting has psychological issues.
But your position appears to be that Bob's statement is no evidence at all.
Your repeated strawmanning of my position is not conducive to reasonable debate.
From Julian Sanchez, a brilliant idea unlikely to be implemented: