Guess what BMW's own RPA tire pressure monitoring system (not the TPMS/RDC system) uses to detect low tire pressure? Wheel speed.
It sees a wheel traveling slightly faster than the others, because it has a small diameter, indicating a tire down on air.
You just told everyone tire diameter is not affected by tire pressure. I'm not sure how helpful you're going to be...
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'02 S54 M3 (500/500 GC/Koni)
'08 N54 135 (JB4, DCI, BMW PS/Bilstein B6s, H&R M3 FSB, Strongflex FCABs)
'14 N55 X1 (JB4, BMS DP, BMS Intake, Alpina TCU reflash, H&R Sports, Bilstein B6s, E93 M3 RSB, Strongflex FCABs, baby seat)
'08 N54 535xi touring (Bilstein B6s, Downpipes, MHD tune, baby seat)