All 4 tires must be same diameter?

I took my mother's Forrester to be inspected, and the shop reported that one tire was damaged and needed to be replaced. They also said that since the car is all wheel drive, I had to find a replacement tire that had the same amount of wear as the other 3 tires - either that, or I had to replace all 4. Any validity to this?

Diameter the same, correct. But exact same wear is a stretch unless the other three are bald. But you do want to have the same level of traction/grip for the AWD. Rule of thumb is replace all four if less than 25% tread remaining. Check the owner's manual and I think Tire Rack has guidance around this on their web site.

But will a small discrepancy in diameter destroy the diffs?

No.

 

A small difference in circumference can occur just from a couple of psi difference in tyre pressures. Don't sweat it.

http://www.legacygt.com/forums/showthread.php?t=105336

the thread above is true. the old-techs where i work at always say the tires must have a remaining tread withing 1/4" of an inch.

 

you will need to mount the new tire and check the diameter of the new tire and compare it to the other ones while the car is off the ground and the tires properly inflated. 1/4" is the limit though so anything more can start to cause damage to your drive train especially at highway speeds.

if you measure the tread depth of the other 3 tires, tirerack can shave a new tire down to the same size for you before shipping it.

Thanks for all the great information, as usual.