I'm not sure if it is necessary or not--but anyone on a cell phone could claim they are the parent, couldn't they?
If they call us, correct, they could be anyone - and we won't/can't talk to them, but if WE call THEM (using a number the adult in charge has provided) then yes, we'll talk, explain procedures, obtain consent, the whole works.
If the adult caring for the child hands us a phone and says, "This is the parent," we'll believe it, but if some random person calls us and SAYS they're the parent, then sorry, unless someone present who knows them talks to them and confirms their identity we can't tell them anything at all.
We had a wreck just a few weeks ago where a total of THREE different guys called trying to get info, all claiming to be the father, PLUS a FOURTH guy who showed up in person.

I felt like I was on that old game show, To Tell The Truth.
Turns out they were all family members who wanted information and knew we wouldn't give it to anyone but a parent, so they were purposely lying...but they had us really concerned that they all really thought they actually WERE the father! (btw, none of these 4 guys was the actual father!)
If there's a life or limb threatening emergency, we can treat without consent, and if it's not an emergency, then there's almost always plenty of time to contact the parent.
A letter is fine, but a list of numbers where you can be reached 24/7 is even better.
