Is a full haircut truly necessary for baby’s helmet to fit?

My son is 5 months and our doctor has us seeing a physical therapist and cranial tech for his head and neck. His head is a bit flat on one side so we’re getting fitted for a helmet. He’s had long curly hair since birth and the doctor at cranial technology said we have to cut it in order for his helmet to fit correctly 😭 Has anyone else had this happen? She told us we can try to mold the curls down but told us if it’s too long or curly they may have to send us home until it’s cut.