Think of this scenario. What happens when someone sits in the back seat of a car? That compresses the rear tires slightly, imparting a slightly a different radius. Many cars will ask you to increase rear PSI to compensate, but nobody ever does. Are diffs failing for this? Nope. AWD cars and trucks manage carrying a random number of rear passengers just fine without any adjustment to tire radii.
If you have a torsen or similar FWD car that only engages the rear wheels when slip is detected (most Audis with transverse mounted engines, VWs, etc), then you're fine.
Tire diameter in passenger cars does not change with loading.
Besides, regardless if it's a myth - doing it will void your warranty, it's a requirement in every AWD service manual, and any tire guy caught doing it will be held liable if your diff blows up later. No mechanic or tire shop will agree to swapping out just two.
The manual probably also says that aftermarket oil/air filters will void warrantees, or that changing your own brake pads is dangerous. Total bunk.
> Think of this scenario. What happens when someone sits in the back seat of a car? That compresses the rear tires slightly, imparting a slightly a different radius.
The tire radius changes, but that doesn't matter. What matters is the rate at which the axle turns relative to distance covered, and I doubt that changes significantly with loading.