Is it safe to run the oversized staggered wheels

[mejim707]

With my recent debacle after replacing the transmission and having a very nasty shudder / shake / jerking form a few weeks following, I brought my car to BMW who diagnosed that the transfer case front wheel drive chain was worn out and had a lot of slack in it causing the issue.

They told me that running larger wheels and tires was why this happened. However, I'm running the sizes that BMW suggests are ok for my car.

Fronts: 275/40/20
Rears: 315/35/20

I didn't think this would be an issue since it adheres to BMW suggested sizes but the master tech told me only the M series X5s can run these size tires because of the programming of the computer. They also quoted $8500 to replace the transfer case which seems like a fair and reasonable price and not at all a laughable quote lol

So, is it safe to run this staggered setup on an X5 that is not an M package?