I've chaperoned at least my share of trips with high school kids.
As much as I would choose to have one anyway, I agree that in a crisis, the letter from mom and dad wouldn't be absolutely necessary in terms of saving a life-- ER staff will do whatever is necessary to save a life.
I think the difference is what goes beyond that-- what they're able to do in terms of pain management without written permission. They're not going to give so much as an aspirin unless they're confident that the patient doesn't have a known allergy.
Likewise, if the child is unconsicous, he isn't in a position to talk about his allergies. You may know that he's allergic to strawberries, but I would want it in writing that he's allergic to Avelox or Cefzil. I would assume that medical personnel would want it made very clear--in writing, and not take his word for what the allergy was.
And if the friend is a teen, and the boys are likely to spend some time without parents, then a photo ID is necessary.
And, as much as we sometime don't realize it, we're not all available 24/7. Sometimes we're in the shower, or swimming, or the phone is home recharging, or we're at a meeting (or, for me, in class) or at church, and the phone is turned off.
I've spent time in ERs in Pennsylvania and Chicago with other people's kids. And in2012 my husband landed in the ER while at WDW.
At the end of the day, you go with what you're comfortable with. As a teacher, I tend to lean towards "more is better"- the more info I can have in case of a problem, the better I'll sleep at night while chaperoning other people's kids.