The gods are smiling on your and you have good karma! Keep on rolling Breadboy...your stories always put a smile on my face. Ever had a sunroof leak? LOL....see my post further down.
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1998 S70 T5 Emarald Green Metallic, 2004 V70 2.5T Ruby Red, Previous Owner of Black '94 850 Turbo Wagon. My cars have been running so well lately they've got me worried.

wow 415k and not even changed the oil in the difs?? - whats the vehicle?

sorry guys i cant agree..

the diff (on the axel) is there to allow the wheels to turn at differnet velicitys when cornering ...not all the time.... so if you have differnt sized tyres on each wheel your essentially going to exceedthe duty cycle of the diff...and heat the fluids etc up.. at the very least you will get accelerated wear..at the worst....well lets say it might not be pretty! You may also stress the central diff too.....

I have no idea if these cars have locking diffs (aka propper 4wd) if they do even on the loose stuff mismatched tyres are a serious no no.....

of course its only my 2c and arguably worth that but i wouldnt risk my several thousand $ worth of over complicated over electroniced 4wd sytem for the sake of the cost of a couple of tyres....

oh and 1.5cm assuming a 22" diameter wheel represent just under 1% in difference in rotational speed....

I like your math and respect your judgement in wanting to replace all 4. But 15mm = 1.5cm = 3/4inch, and that shouldn't be enough to warrant the computer or sensors to engage slip control. Just having tire pressure off by 5lbs on one wheel would do that also.
If he were to put the new tire on the right front, it wears the quickest on my car btw, then he should be good to go.
It's not like putting on a space saver spare and driving 30 miles to the closest service station, that will cost $$$$. Which is why I now joined AAA.

Klaus
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(V♂LV♂s 1975 164, 1995 854T, 1998 V70R)

It's not going to do anything to a diff to always have one tire on one side bigger than another. Nor to a WWD center diff for the rear tires to turn less than the fronts (which they always do, in fact, because rears always follow a tighter turn than fronts) -- what you don't want to do is drive a 4WD with the center diff locked, or in some 4WDs (like my 460 Gelaendewagen) without any center diff, on dry pavement.

Rather than a strictly mechanical thing about the differential, it's a concern of the pumps and other controls that diverts torque to the differentials. The reason for mismatching concern is for there to be a continuous signal of different speed which is going to have the AWD system continually thinking that there is wheelspin (or slippage) and trying to divert power (as it compensates for this alleged slippage).

By the way, you're 100% about this sometimes being a problem with 2WD cars. About ten years ago, Mercedes sedans with a certain antiwheelspin software would, when faced with mismatched tires, put the engine in low power mode (to lessen torque output) and the car would suddenly just go slower, and slower, and eventually just barely crawl down the road regardless of how the driver stomped on the gas pedal!