Contrary to what expat lore says, the charge in question is not a fee for having your vital signs taken. It is a charge for use of the hospital facility. The consultation fee goes direct to the doctor, who in a private hospital is a private contractor, not a hospital employee. The hospital adds a charge for use of its facility. Everything from electricity, waiting room, building maintenance and repairs, , housekeeping, appointment scheduling, medical record keeping etc etc etc as well vital sign check. It is a flat charge not individually adjusted.
In Thai the word for hospital is "house of nurses" often shortened to the word for nurse. So "nurse charge" = hospital charge.
So yes. they have every right to still charge it.