What exactly is their problem. The car is under a BMW warranty, and regardless of what the problem is, they're liable since they've performed (or lack thereof) all the work. No fluid change or wrong fluid, whateva..they at least owe you a new diff since you've got the warranty.

Easy to find out what exactly happend. Take a sample of the fluid in the diff right now, and also send a reference sample (a new bottle of bmw diff fluid) to be analyzed. It won't cost you more than $50, and it'll give you a definitive answer to the age/condition of the fluid, and whether they used the right one in case they did change it.

These guys are a pretty big and popular lab. I'd give them the headsup of what's going on before you send it in, so that they pay attention to what's important to you: http://www.blackstone-labs.com/