Ok, I think I will be the sort of minority here-It would depend on the circumstances and the kid. I grew up in Wyoming and Colorado in the mountains and around horses. By sixteen, I had been on numerous back country backpacking or horse packing trips as had my brother, and as have my sons. My brother and his best friends took a trip exactly as you describe between their junior and senior years of high school in Yellowstone and Grand Teton Parks and had a great time. They fished, hiked and slept in the truck instead of a tent because it was less work. Yes, they chased girls but not seriously and they probably drank beer, although they never admitted it and they knew better than to drive if they did.
For the right kid in the right circumstances no problem-for one of my boys I would say yes-he is well versed in emergency procedures and familiar with the wilderness, and even what to do in the event he ecounters dangerous wildlife (of the 4 legged varity at least). The other one is a city boy through and through and there is no way I would let him do this even if he wanted too.
You know your son and whether he can be trusted doing this or not better than any of us.