Cavemen was a very clumsily produced and written show, and I tend to agree if they did the same episode, it would have been poorly written and offensive outside its intent.
They really managed to make the show with in a show subtly terrible, and they really managed to get the nuance of how terribly sitcom character tokens/wacky broad stereotypes usually are. Especially 1990's gay friend characters, or basically everyone in Two Broke Girls. They really handled this episode well, showing Zorn being actually hurt and offended and basically turning it all on him. But to me, the key scene that took this episode from sitcomy to heartwarming was the end bit where the mother tells Allegulon why this stuff is important and the significance of everything that was just embarrassing. Also adding to his girlfriend being more offended by his actions than Zorn's culture.
And by the employee that felt bad about insulting Zorn taking him to the very same insulting ethnic restaurant as an apology. His reaction of "*&^& it, but this guy means well" was just delightful.