Even stranger than the origin of the Saturn V coordinate system is that of the lunar module:
The X-axis station reference measurements (inches) start at a design reference point identified as station +X200.000. This reference point is approximately 128 inches above the bottom surface of the footpads (with the landing gear extended) ; therefore, all X-axis station reference measurements are +X-measurements.
LMA790-3-LM Apollo Operations Handbook: Lunar Module
As seen in this diagram, this places the origin of the coordinate system 72.85 inches below the bottom of the footpads that rest on the moon's surface, and 5.35 inches below the tip of the touchdown sensors. In other words, the origin of the coordinate system is outside the spacecraft and "underground" when on the moon.
Why was this reference point chosen?