I would guess it’s more to do with tire thickness and flexibility than the volume of air. A MTB tire is quite a bit thicker than a road tire, a car tire is a helluva lot thicker than a MTB tire. Volume of air would only be significant if when you push on the tire you are significantly decreasing the volume (and therefore increasing pressure). Even with a 23C tire the volume reduction from you pushing it in a few mm in one spot is going to be negligible.
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