It's not a back-formation. I agree with Faldo. It's just a newly coined word that uses bits and pieces that originally came from Latin. I wouldn't call cherry and pea mistakes either. The term in linguistics is reanalysis. The -s at the end of the singular of those words was reanalyzed as the plural marker, so the new no-s-ending singulars came into being.

Ceci n'est pas un seing.