No, I don't think that strategy works for anyone else. That's working because of identity politics. There are people who feel like this is their voice, their only voice, and they're going to refuse to give it up, whatever that requires that they tell themselves.
I just don't think that applies to a chef. Not many people are that invested from an identity standpoint. How many people even go to a Batali restaurant a year anyway, let alone would identify being a fan of Batali as one of their main driving traits?
Someone like that is going to get dropped from the media either way, deny or not, so there's no sense in denying.
Probably sports, and maybe a very small handful of niches in the entertainment world, will there be so much personal investment in a personality that denial could be worth it.