A few thoughts and questions:
I assume you know that in order to be played, a file has to be read, right?
Would it be better if the question wasn't asked? I'm not sure of the right answer to this one. For example my computer doesn't ask this question. It simply provides the access. If I wanted to prevent the access, I could set up multiple users with private directories and make sure to only use known-safe apps in the user account with the private data, but few people (besides governments and corporations) seem to bother with stuff like that.
For a typical user, I would say that if the stuff is that private, then never play/read it on anything that is connected to a network. For example I could play a secret file on my TV or my BD player, since neither have network connections.
