This is one of my all time favourite, but reading this again I just realized, how the fuck did the rumour get as close as: "school girl in uniform stole your iris" and not have them know it's Kuga?
You either have no clue who's doing it, or the person who's lost their iris can recall it happened after Kuga talked to them and made them realize something. Then immediately that person who just lost their iris can finger Kuga out as the Iris Hunter. At no point would this ever organically evolve into the "school girl iris hunter" rumour.