In answer to the OP, yes it is true.
I am unaware of a scriptural basis. But when I was at Bethel, I was talked to informally about my haircut being too low, shy of being bald.
I also know of a brother personally, who was at Bethel when I was, that was counseled about this. He was a black brother. He would give himself a haircut rather than go to the Bethel barbershop. He shaved it off several times until he was talked to. And he personally told me he was counseled.
I found it strange at the time, but it wasn't enough to make me question the "slave".
CoC