I think there's a higher than 50% chance that the dad is lying but fair point about the rarity of this phenomenon. I am certain its a legitimate phenomenon but at the same time to what extent has the discourse on the issue created a kind of copycat effect? I remember reading about how
Dissociative Identity Disorder was pretty rare and when it did happen the average number of personalities was like 2-3. But then
Sybil came out and there was an increase not only in the number of DID cases but also in the average number of personalities in each case(the character Sybil had like a dozen). I think its possible something similar is going on here.