Actually I think you have that entirely backward -- having been worshipped for such a large percentage fo their life, I'm willing to bet they feel the jabs every bit as much as we do, perhaps more. Some get jaded, and of course ironically the same fans who made them jaded then pile on them for becoming so, but some do not. And in Webber's case he was clearly hurt.
I think its closer to the truth that fans make up the excuse that players don't feel so they can justify their insensitivity to themselves. "Oh, yeah I'm being an *******, but its ok, he's not human, he's just a player." Fans like being *******s -- sports give them an outlet to let out their inner jerk in a way most hopefully would never do in the rest of their life.