I bet it's fixable, just doesn't make sense that this would be broken forever because of some "testing" your console is used for as preview member. Hope you don't have the newest firmware on your controller and that this is the reason, if not there has to be a solution on the internet since this would have to be a common thing if two in this thread had it already.
At the time of it happening to me it was a very isolated problem, I literally found one other person with the issues on they're help forums. That was around 6-8 months ago, maybe there is some crazy solution to fixing it. But like i said its the risk you take when beta testing a product, when you sign up to these things it would have said theres a chance that your product could completely fail.
I know that, but they have to say that to be safe, normally it still doesn't make much sense that a console will be broken forever because of some beta program you are in to test some updates before they are made available for everyone.
Just read some stuff on the internet, many had issues with their controllers while playing FH2 but it's hard to find much about "the sync button of my console doesn't work". Would be interesting to know if it's the button of the console which has no function at all or if it works but he doesn't recognize it because his controllers don't connect to the console.
If he has Kinect he can try to connect the controllers with Kinect. If that does also not work I would think it's the controllers firmware and not the XBO itself which doesn't work with whatever beta program is on the console right now.