A friend told me (Subaru) that the variation in tread depth on the tires cannot exceed 2/32, otherwise the differentials will wear out!

Is there any truth to it, or a tire salesman myth?

 

If you run it with more than a .5/32 variance between tires, your car will promptly explode upon ignition.

 

I instructed my car to stop running around.

According quote below, the correct number is "4/32 of each other in remaining tread depth".

There are several suggestions that have been offered to drivers who are replacing pairs or individual tires on their four-wheel drive and all-wheel drive vehicles. Some vehicle manufacturers recommend that all tires maintain the same rolling radius and circumference, while others suggest that all tire circumferences remain within 1/4- to 1/2-inch (8/32-16/32) of each other. Other vehicle manufacturers recommend that all four tires remain within 2/32-, 3/32- or 4/32-inch of each other, or within 30% of each other in relative

Audi: As published in their vehicle owner's manual, "rolling radius of all 4 tires must remain the same" or within 4/32-inch of each other in remaining tread depth.
Porsche: Cayenne within 30% of the other tire on the same axle's remaining treadwear.
Subaru: Within 1/4-inch of tire circumference or about 2/32-inch (1.6mm) of each other in remaining tread depth.