Ok, so such a thing as the "parallel of origin" does seem to exist, but it has absolutely no practical purpose. Unlike the standard parallels, it is not used anywhere in the mathematics of the projection.
Instead of saying "scale is smallest at the parallel of origin" you could just say "scale is smallest along that parallel that is mid-way between the standard parallels"!
I'd most likely think that it would be used in the "mathematics of the projection", but not sure how and don't really care.
Really don't understand why you would want to make the explanation any more wordy than what it already is... just seems to complicate things.
But at the end of the day, not really practical for hands on flying. Just know how to read the map.
Some good info here
Jar professional pilot studies - Google Books
Knox.