Wow, I'm glad that I went with Geico's mechanical breakdown insurance. You must purchase in the first 15 months/15k miles to extend the warranty to 7 years/100k miles. I felt a little bit like I was getting ripped off a bit having "double coverage" for those first 4 years/50k, but after hearing so many people having BMW reneg on their warranty, I can't help but think that I'm lucky to have a second warranty that reportely NEVER tries to get out of the repairs.
I hope that you can get some assistance on this issue. Even with a minor impact (scratched gas tank yet the diff bolt sheared??), it sounds like a normal type of road use. You weren't autocrossing/off roading with it, right?
ANY vehicle should stand up to normal use, even the occasional cardboard box on the freeway. If it's not substantial enough to rip off your front bumper, etc., on the way in then it shouldn't be substantial enough to rip off your differential.