Boy, does *that one sound like a folk etymology.

Yes it does. Most relate genuinus 'innate, native, natural' with the same root that noun genus 'race, stock, breed' and the verb gigno 'to beget, bear' come from. There is another word genuinus in Latin which means 'of or belonging to the cheek' (dentes genuini 'jaw-teeth, back-teeth') from gena 'cheek'.