[mooders]

What does the user care about? In your example, I guess they care about bandwidth usage and personal data. So in that light, I would inform them that a small amount of game-specific, non-personal info needs to be sent to the website (server is jargon, so should be avoided) to record the score.

My point is that as much info as the user cares about should be provided in a clear, accessible manner.

Where personal data and/or legal disclosure laws apply, then more transparency and info is better.

Unfortunately, it is not unnecessary to point out that all information of all types at all times should always be rigorously honest. If you're going to tell your users something, be truthful.