Request? You appear to be implying that the doctor has the rightful authority to make your decisions for you unless he chooses to allow you to make another choice.
Hypothetical: If your child was on a vent, or on bypass; you can't leave AMA without security/LEO intervention as by disconnecting the patient they would die.
Similarly, if a person cannot speak for themselves; and the POA/Guardian is making a stupid decision regarding healthcare. Health care personnel can request an emergency guardianship hearing for the well being of the patient. Having been involved in these sorts of things, it's not as simple as black and white, and in order for the "hearing" to take place, there typically has to be imminent danger and/or negligence involved.
My words are being twisted for some sort of anti-CPS/State/Hospital argument.
The doctor's and especially nurses are not advocates for the parents, but for the patient. If you're going to do something stupid that could harm your kid, and they DON'T do something, they can be held liable civilly and criminally.
They were just doing their jobs and CYOA if you will.