Actually, research into the nature of humour has found that one of the important conditions for something to be “funny” is that the person perceiving it has to find it somehow harmless, so sort of the opposite. (Another key component, which you may have been mistaking for “offensive on some level,” was a twist on or upset of expectations, i.e., the punch line.)[/quote]
Humor works in an overlap between offensive and harmless. A totally ridiculous joke like “What did the robot say to the centipede? STOP BEING A CENTIPEDE!” aren’t funny because it’s not offensive on any level. “Why was Hitler okay? Because Jews are evil!” Isn’t funny because it’s just… nothing but offensive and pretty fucking antisemitic. There is an overlap, though, that differs for pretty much everyone.
I also think it’s ridiculous when people get offended on other peoples’ behalf. This happens to me waaay too often, but that’s neither here nor there.