XBOX Live Compensation?

Thought the coast was clear, that Xbox Live had finally fixed it's problems, think again. There are ( even as I write this post) people out there who are still having the same problems with Xbox live that they were having last week. This is the message that came up on the official Xbox.com website.

Users may experience issues performing transactions dependent on Windows Live ID availability including but not limited to Xbox 360 account creation, renewal, recovery, and logging into or creating Windows Live ID accounts. We are aware of the issue and actively working toward a resolution. We apologize for any inconvenience.

Apparently things haven't been fixed as everyone was assured it would be. A good portion of the problems seem to be associated with the marketplace and trying to purchase content. Some gamers have reported losing Microsoft points, not being able to complete their transactions, in some cases causing achievements to disappear and not being able to connect to specific multi-player games such as Halo 3 and Call of Duty 4.
In light of these problems Xbox has said they will be compensating Xbox live users with a free game from the Live Marketplace. I have a question about this "token of our appreciation", will customers be able to choose the free game they want because what if the game that Microsoft is offering you've already purchased, what then? The least they could do is offer a selection of games to choose one from, I hope that's the rout they take. Please comment if you have any thoughts on the situation.