I'm not sure if the GXP is set up the same as my GP in the back but I'd suggest getting the car up on jack stand and start tugging and pulling things around. You could start with the wheel on and check for any play. Then you could pull the wheel of and start lightly wiggling things around. Progress to violent shaking and you may find something.
I found a rear sway bar end link with play in it just by wiggling stuff around. It would rattle when backing out in my (rough) driveway.
If they said "that tire" will cause problems then there is likely something wrong with the tire itself, out of round/out of balance etc. If you're buying new ones I would sweat it. Just my thoughts on your issues - not gospel!