Nc for this
My ex did very similar to my dd when she was 10 because she had a (very mild) case of nits - which were being treated.
Dd was DEVASTATED not even exaggerating, the entire weekend after I got her back before her going back to school on the Monday I had a very tearful, heartbroken anxious child on my hands. I tried my best to reassure her, showed her lots of pictures of actresses/singers she liked with short hair, told her how gorgeous she still of course looked, that it would grow back soon etc etc
None of her girl friends had short hair, it had been waist length before, first time she'd ever had nits and she's not had them since. Hair was looked after just one of those things that happens sometimes.
She was worried she was going to be teased and called "a boy" (she wasn't wrong, conservative area we were living in at the time).
In addition the way he went about was awful, was brushing her hair and just without warning grabbed a pair of scissors gathered it in a sort of ponytail in his hand and just lopped it off! Then took her to a neighbour who USED to be a hairdresser but hadn't been for some years to "tidy it up" it was a fucking mess!!
Dd wanted to call me - he wouldn't let her.
It REALLY SERIOUSLY affected her confidence, she had nightmares, she wouldn't even sleep alone because she was worried when it started growing he'd break in to cut it again (yes I know that was irrational but it's how she felt).
I then had major legal issues because she didn't want to see him/visit him again (understandably) and there was a contact order in place.
Thankfully it didn't have to go to court I think because his solicitor made it clear he'd been in the wrong. Very very gradually the relationship between ex and dd was rebuilt but he ruined what had previously been quite a good one. Idiot!
So yea - I definitely think it's abuse. (If not a hoax) and if true then I think the reason a 13 year old would aquiesce is because this guy is ALREADY very controlling if not physically abusive.