I suppose these groups take the name "Catholic" to draw away real Catholics who have not yet been lured away from Protestant sects that already teach the same things.

Wasn't the Catholic Church established by Christ and continues in the passing of the papacy from St Peter onward?  And if so, then isn't wherever the Pope is, that's where Catholicism is, even if the Devil has infiltrated the papacy?  Jesus never said "Catholic;" so if these schismatic churches believe that they are correct, then they believe they are correct about Christianity, not Catholicism.  That is, they are Protestants.