People do believe it, because thinking that intent matters makes it impossible to defend their other position: that the most important thing is how the "offense" is received.

If intent matters (as you say, anyone with half a brain knows it does), then if you receive my comment as being offensive, I am still right because I didn't mean to offend you. What they want is to make sure they can tell me I'm wrong anyway because the person was offended... hence, my intention didn't matter.