People are often confused by 12 AM/PM but I am confused by your statment that it “can’t be either.” Noon by clock is specifically 12PM. Midnight is 12AM. If you meant to say it “can be either” this would also be incorrect.
I’m going to take a WAG, but I’m thinking that the caller was meaning that as something of a joke. I’ve never heard of a ‘low noon’ per se, though you could assume there was one since there’s a ‘high noon’. It sounds like the caller was trying to be funny, but then they were taken seriously and so they kept asking.
Another vote for “the customer was being a jackass.”
I encountered one of these when riding along with a musician friend to a gig. We had some trouble finding the right building, and when we thought we had the right one, I hopped out of the car to go see. The place was locked up, so I knocked and this guy came to the door. I said, “Hi, I’m here with Friend who’s playing here tonight. Are we at the right place?” He says something like, “Well, are any of us in the right place?” I gave a small chuckle and said something like, “yeah, well, is this where we should be?” “Who really knows where they SHOULD be?”
I wanted to strangle the guy, but I had to be nice because I was “representing” my friend. Look, buddy, we just want to know if we can park the car and unload our stuff. Time’s a-wasting. After a few more rounds of this nonsense I finally ascertained that yes, this was the place.
I run into this type of jerk far too often. Yes, hardy har har, you made your lame joke. Now can we conduct our business?
I did, in fact, mean that “p.m.” means post-meridian, “a.m.” means “ante-meridian”, and noon IS the meridian, so it can’t be either.
I have heard very heartfelt explanations for it being both, however (the above example of “12:01 is pm, so 12:00 is, too…” being countered by "the clock goes from 1:00 to 12:59; 1 in the morning is obviously a.m., so 12:59 (eleven hours and 59 minutes later) is, too; noon, being within that time span, is obviously a.m.).