I don't think you are using that correctly, you seem to be using it as a synonym for jealous/hater. I don't get the impression Aaron is disparaging fame or success; he is making the claim that Mark Zuckerberg has a questionable moral compass. That really doesn't relate in any way to the Aesop's Fable you reference. The fox didn't claim to dislike the grapes because they were ethically dubious; he disliked them as a way to feel better about not being able to acquire them.
I know it's a movie and not necessarily based on actual events, but people like this always make me think of the line in the social network: "If you had invented Facebook. You would've invented Facebook."