Special correlation ignores circles too, which includes Killer Instinct. Circles, killer traits, and sigils not working isn't really indicative of a monster not being a certain family in all cases; an otherwise inexpiable 25% boost in damage of an element whose damage modifier is quantified, however, is much easier of a thing to see and believe as an indicator of family.
I'm not entirely sure why special correlation exists, we'll have to ask a scientist, or a psychologist. Either one probably won't have an answer, but it's worth a shot.