Excellent points. However, many people when saying "That is offensive" don't just mean they are offended; they are implying that all decent people would be similarly offended, that what the other party said was beyond the pale. So it is used, in these cases, as a sort of one-place function and an attack (sometimes personal) against the speaker.

It is still true that escalating with complaints of censorship, PC thought police, etc, is not a good strategy for making the situation better and more conducive to a reasoned discussion (though it might be a good one for the purpose of rallying one's side against the Enemy).