I can't speak for black people - lack of qualification, so to speak -, but I wouldn't be surprised if they considered it offensive. It's perpetuating a stereotype.
It's a benign stereotype as far as that goes, but it still does. It's also a joke I'd restrain to people I know fairly well - it veers into incest territory.
None of that is to say that I'm terribly offended by it myself, but I can see the potential to offend. And as such would reserve use. That's really what all this is about - try to respect the other person at the receiving end. And if you don't know them, try to be as considerate as possible.
Not because telling one such joke per se makes you a bad person, but because it might offend somebody who is not you or not your background. And because the courteous thing would be to try not to offend.
If you told it to me as an actual joke (not as an example as here), and assuming we'd have never met, I'd probably reply with a "Dude, that's kind of not appropriate. Please don't go there". If you told it to me in a large crowd of your friends, and I'd be alone, I might choose to not respond at all, or let somebody else handle this. It's a sad fact that as a woman, calling out inappropriateness usually means you get a lot of flak, quite frequently threats. (See what's happening to Adria right now).
I'd assume that's why she opted for a public shaming. (The appropriateness of which is a whole 'nother topic. I was not comfortable with that, either.)