In the case of the quote, the M stood for meters I'm afraid. So GPS will have that added to its currently speced. uncertainty.
In an old Practical Sailor test of sextants some years ago - the accuracy of the average fix of the 6 testers was slightly less than one nautical mile, dismal by the standards of GPS - even degraded with sun spot interference.
I certainly respect your celestial navigation ethic (and skill), but sadly the "scorn" of your stinkpot friends will likely remain.