I think anyone with media exposure is what you might call a passive role model, versus an active role model.
To me, a passive role model can be anyone with media exposure (TV, radio, Internet, whatever), where in any case that person has an audience observing or listening to them. They may not be out there because the are actively trying to be mimicked in some way, but nonetheless they do have ears and/or eyeballs on them, and at least some people (probably mostly some children) are prone to taking something from their behavior and then mimicking it themselves. The whole monkey-see-monkey-do concept I used to hear as a kid. That's not their fault, and they didn't do it for that reason, and I don't feel they carry a high degree of responsibility for it, but I think it does exist.
Then you have active role models, the people who deliberately want people to follow their example. Being a big fan of the character and those films, I immediately think of the fictitious example of what Bruce Wayne was trying to do by being Batman in the Nolan films; he wanted to inspire people to resist the state of things in Gotham (the corruption, the crime). He was an active role model who was deliberately theatrical to gain attention and to hopefully inspire good. He was an active role model. His actions would carry a much higher responsibility with regards to being a role model because he's actively bringing it upon himself on purpose.
Something like that, anyway.
Getting back to passive role models, I think they have some degree of responsibility in so much as they have to know that impressionable people (again, mostly some children) are observing them, and that if they act a fool, that might have a negative impact on someone like that (although I can't imagine it ever being very serious), but I think that only goes so far before you have to give them a pass. They are, ultimately, out there to earn money playing a sport, not because they deliberately wanted to be an active role model or were trying to inspire people, and I don't feel they're strictly obligated to do anything in that regard, though it's certainly good if they do and probably a good idea.