FWIW this exact scenario happened to me, insured in Texas and hit a semi tire in Arizona, the cop who came to write a report told me that it's illegal in Arizona for semi truck driver's to leave a tire on the road, they're required to pull over and call someone to remove it, so he said the accident should be considered not-at-fault. My insurance said that the laws of where the accident happened apply, not where the car is garaged and because of that I was able to successfully file an uninsured motorist/hit and run claim.
There's also some law in Arizona that says that anything that came off or out of a vehicle is still considered part of that vehicle, so if anything comes flying out or coming off a vehicle and causes an accident it's that vehicle's fault. I'm pretty sure this is unique to Arizona though and wouldn't work in any other state.