I took my "new to me" Fuchs in for new tires when I got them, and what happened almost made me choke the guy mounting the tires.
When he was removing the old tire off the last rim (I was hawking him like a mofo), he must not have mounted the rim on the machine very well, and the rim and tire popped of the machine and went rolling 5 or 6 feet. I noticed it landed cleanly on the old tire so it was not so bad...
The guy picks the wheel up and puts it on the machine and starts. I'm thinking it is OK, it didn't look so bad and let him proceed. It happens again! At that point I am worried but don't make a move for the guy ("restraint Grass Hopper") (hey they're the most expensive thing I bought for the car next to the motor...and I'm a cheap SOB).
I let the guy finish and inspect the rim, no damage that I could tell, but a couple of small shallow scratches that I couldn't remember if they had been there from before.
I'll always take the rim in, but I will definitely be more instructive about their handling...hell I don't have 5 or 6 sets of Fuchs like some people I know (you know who you are

).
Plus, I get to torque them myself which gives me a warm fuzzy.