I'm pretty sure you were on the right path but convinced yourself otherwise. Yes, the diameter will change. Circumference is 4*pi*D. So the circumference will change. So, for every 10 feet of travel, the wheel with lower tire pressure will rotate more than the wheel with higher pressure.

The ABS system measures wheel speed, and will notice this difference, and show that you have low pressure.

This does not work when all 4 wheels have low pressure, because they would be rotating at the same speed.