No, you’re thinking about a different scenario. What matters is not if you are black, but if you are the target of the word you are comparing to the n-word.

She, as an obese person herself, proposed that “obese” is equivalent to the n-word. She didn’t censor her word the same way a black person doesn’t have to censor the n-word. That’s not a contradiction. It would be, if she wasn’t obese.

Not that I care about the actual point, just wanted to talk about the logic. My bad, if my assumption that she is obese, is wrong.