When you first use an Xbox enabled game from the Store, it first asks for permission to modify your Xbox Account Information, stating that you can change this from the account settings.
Which account settings do I need to use to change this permission?
The settings in the games themselves don't include this (usually it's just "Notifications" in the permissions tab and "This application can use your internet connection").
Checking in the Games app, there's no list of apps that can interact with Xbox account, and I also can't find anything in the xbox.com account area.
The behaviour is consistent across computers - so for an account that has denied access on one machine, that state is replicated to other machines for the same game.