For the T-case, the concern is the different revs per mile front vs. rear. But side to side differences can be also be tough on a differential. We had a T-case start to whine on our X3, and the dealer cited the Goodyear Eagle F1 setup that had too many revs per mile difference between the front and rear on the staggered setup. It was the correct sizing for the wheelset, but each brand of tires might have slightly more or less revs per mile ratios. OE tires tend to have less of a % difference, and that's likely not coincidence. Long way of saying that the tire store is making up a story, but hard to tell how material it is. Heck, you can probably adjust revs per mile readily by tire pressure settings.

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2016 GMC Sierra 2500 HD All-Terrain, Duramax 6.6

2011 X5M Alpine White/Sakhir Orange, Eucalyptus, Spare tire!, Comfort, Soft Close, Tech, Rear Climate, Individual dash, Individual Audio, HUD, DVD, USB, Cold.

Gone:
2008 4.8i
2005 X5 4.8is
2004 X5 4.4i Sport
2004 X3 3.0i 6MT
2002 M5