Frank Kogan

Depends how strict you want to get I guess. SNSD's Jessica is known for being an 'ice princess', aloof and arrogant. That has earned her antis, but also lots of commercial interest. Of course she's not actually arrogant in public, she's nice and friendly and pleasant in many settings, but may talk a bit less, smile a bit less than your average idol. Her sister Krystal in f(x) has gotten a lot of flack for being arrogant, like several actual articles with quotes from insiders saying she acted like a diva on the set of some commercial or photoshoot, or that she was rude on a tv show, but at the same time the sisters are more often pitched as being 'cold girls' in a chic cool way.

Other idols have a similar reputation or image. 2PM started out with defiance of the rules and brattiness as their 'concept', but after the issues with Nickhun leaving they toned that down. Anyway that was different, more of a game.

Of course if this translated into public acts of defiance against their fans I'm sure their status as idols would be in danger.

(Interview with the Jungs: http://soshified.com/2012/06/marie-claire-magazine-interviews-jessica-and-fxs-krystal

Jessica: Because I’m the type who expresses my opinions honestly, my first impression seems to be taken sharply. I’ve caused misunderstandings a lot, but I don’t try to change myself because of that. Isn’t being honest better than being fake? I just think they’ll get around to understanding my honesty some day.
Krystal: Guys don’t really like me. Guys like girls that are kind and innocent. I used to be innocent (laughs). Now I’m not. Plus, it’s not something I want. )