So let's try to make a little more sense of the data
XM and AM work fine
FM is not working as desired
iPod Nano is not working as desired
The radio antenna is in the back window
The car has received window tint by a 3rd party
If the 3rd party window tint is metallic, this could be the cause of the FM reception problems
It makes sense that the dealer is not going to do radio work under warranty until it can be established that the 3rd party window tint is NOT the cause of the problem
Does the Camaro5 community know for sure if the Nano does/does not work with the Camaro(I don't)?
It makes sense that the dealer would first ask, "are you doing it right" when trying to use the Nano.
Get more info on the window tint; consider removing the window tint; and follow the directions for the iPod. Once you've 'done your homework' then fight the good fight for warranty work.
Good luck!