> I must have heard the story wrong.

More likely it's just the wrong story or a garbled story.  There are
so many that make the rounds.  Another story that makes the rounds is
that a "square meal" comes from trenchers, which sometimes were square
boards, dished in the middle.  But not all trenchers were square.  In
actuality, the idea of "square" meaning good or proper comes from
Freemasonry, meaning a true measure.  American English uses a lot of
Masonic jargon, as well as gambling related jargon, as in "You bet!"

16 inches is not far from a cubit, which is the measurement from the
elbow to the tips of the fingers.  Still a bit short, I think, but
closer.  My cubit is 18 1/2 inches.  The body is a measuring tool
you're never without, and so there are a number of measurements that
are based on the body.  Like measuring a horse's height in hands, now
standardized as four inches.

Mike in Sacto