No, that's not exactly right, either. They're people and they get to have lives and use Twitter and do what any other high school or college student does. Yes, they have to be mindful of their public position but tweeting doesn't mean they want the attention.
On the original point, yeah, totally creepy for an older male to reply to a tweet from a young woman he doesn't know.
Twitter is public by default. You can do things like set your twitter to private and only accept followers you know. Otherwise, you are broadcasting it to the entire world.
I would bet that their coaches and athletic departments are quick to re-inforce this as well.