For pratical purposes, isn't self-idetification required to be Jewish? If you don't consider yourself Jewish, then you really aren't the same thing as someone who identifies with their heritage, and pracitices the religion. Ideally you would do so, but some do not.
I know a few people wih Jewish moms who "deny" they are Jewish. They know they are accepted under Orthdox Law, yet they seem to consider the matter irrelevant. For someone who really believes in the religion, this is disappointing, but I suppose its a reality. With me, its on my father's side, so I'd have to convert to be anything other than reform.
What I'm getting at is that there may be a situation, in certain scenarios, of the coach wanting it more than the player does. And if the drive isn't internal, it really doesn't mean much. Its difficult to regaurd such people as Jewish, when they don't regaurd themselves that way, as anything more than an ethnic notation.