Bmw x5 Diff Failure

Hi , i am wondering if you can advise me. I have a e70 x5 3.0 Diesel. I upgraded rims exactly 1 year ago to 20″ staggered Vossen rims . Yesterday the Diff broke and i am in the process of trying to source a new diff .

My mechanic is suggesting that the cause of the diff (rear axle drive) failure is the wider Rims and tyres that i had put on. I am not sure since i see the sport package came with those same sized rims and tyress i used.

Do you agree that the wider rims and tyres caused the diff (rear axle drive) to fail ? I am worried as i dont want the same to happen again.

I will admit that since i upgraded , i normally get the traction light blinking at time when the road is slightly uneven when accelerating.

If you can advise me i will be very thankful.