“From what I can remember about that party...”
The implication is that she was so drugged/drunk that she had no idea what she was doing, which was the point of the “bark” comment. In other words, there was no deep “why” to his question about his “blackness”, it was just something random.
The joke wasn’t racist, unless being nasty about Obamalini’s mother is now to be deemed racist.
If you don’t get the point to “you’re lucky that” as “it could be worse”, you’re either obtuse or purposely posturing as such.
It still works out as racist, if you emphasize her drunken stupor. The upshot being, that a white woman would have to be drunk to the point of passing out, to let a black man, or a dog, etc., have sex with her. The equating of miscegenation with bestiality persists.