I think the humor difference is in fact the reverse.

A lot of American humor boils down to "Hahaha look at them they're so DUMB" or worse "Hahaha look at them they're so FAT"

I hate mainstream American humor because it punches down.

British humor more often punches up (Spitting Image comes to mind, as does the lettuce) and is more often self directed.

And when it is about "Look at them they're so dumb" it's very much more about shenanigans and perfectly smart people doing perfectly stupid things than about "That person is stupid overall and that's why they're funny."

And often is MORE self-deprecating. Americans want to be better than somebody pretty much constantly and a lot of their humor reflects that.