We just had a situation....
A couple came to Belize with their 16 year old and her friend. The father is a State Supreme Court Judge who was advised by the US State Department that you must have a notorized letter from BOTH parents that it is OK for the child to travel to a specific place on specific dates with the names of the adults. (Apparently this is to stop the kidnapping, particularly by non-custodial parents).
They were also advised to have on that notorized statement phone numbers in case of emergency, as well as parental approval for any medical care that is given, and also to list any allergies, blood type, etc etc.
Luckily, they did have this information, as the teenager fell and had to have a cast put on her wrist, and have a few stitches.
I have travelled to Canada with my nephew and always had a medical release and on my last trip with him, we were stopped at the border. We had a letter from his parents, AND I had some great contact people at customs, so we were able to enter the country.
It's better to be safe than sorry.