The other day my friend was ragging on me about W’s mangling of the English language and I reminded him that the word normalcy was “invented” by Herbert Hoover and is now a real word.
He didn’t believe me so, with a fair amount of smugness, I fired up http://www.m-w.com. To my absolute horror Noah et al give an origin date of 1857!! I thought I would pass out.
So what gives?? 
What gives is that you picked up a plausible version of the etymology that does not appear to be 100% accurate. On the other hand, it also does not appear to be false.
The 1857 citation refers to an entry in a mathematical dictionary that uses the word in explaining the parallel or related natures of coordinates on a graph that follow the original coordinates of an equation. It indicates something along the lines of having “normalized” the data. There is a second reference in the OED dating to 1893 that mentions the “normalcy” of women in some mathematical analysis. From this, it appears that the word was coined in the rather esoteric realm of mathematics, not coming into general usage until Harding (not Hoover) included it in a book (probably of his “Front Porch” presidential campaign speeches, but I’m guessing, here), describing the desires and needs of the U.S. subsequent to the Great War.
Since Harding was not a particularly scholarly person and demonstrated no interest in mathematics that I am aware, it would be interesting for someone with more interest in this topic than I have to see whether any of Harding’s speech writers had mathematical inclinations.
Failing that, one might consider that Harding could have been the coincidental co-coiner of the term.