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?

LM coordinate system

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    $\begingroup$ I'm guessing that it was chosen so that (a) all reference positions including the end of the surface contact probes have positive X coordinates and (b) the ascent/descent stage separation plane is at a round multiple of 100 inches. $\endgroup$ – Russell Borogove May 14 '19 at 2:44
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    $\begingroup$ Good grief, the shuttle coordinate system is positive-down with the orbiter's zero ref being 236 inches in front of the nose.... $\endgroup$ – Russell Borogove May 14 '19 at 2:49
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    $\begingroup$ What? The shuttle system makes total sense! That's why these Apollo ones seem bizarre to me. $\endgroup$ – Organic Marble May 14 '19 at 3:09
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    $\begingroup$ I left out the ironic smiley from my last comment... $\endgroup$ – Organic Marble May 14 '19 at 3:28
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    $\begingroup$ That's the floor of the sound stage beneath the regolith simulant. ;-) $\endgroup$ – uhoh May 14 '19 at 5:13

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