I didn't read through, so sorry if someone already pointed this out -
Don't a lot of schools take their 7th/8th graders on year end trips to Six Flags/Cedar Point/etc-type amusement parks every year? We did it when I was in school, and my kids do it now. We certainly didn't have teachers running after us the whole day, nor parents. We were told to meet back at such and such time, and if we were late, the bus was leaving for the 2 1/2 hour trip from Sandusky to Detroit without us! We made sure to get our butts back to that bus on time!!!
DS went to Six Flags with his class in 8th grade, too, a couple years ago - and same thing. They said that the kids better be back in time because any kid that didn't make the bus would be making a phone call to their parents to come get them (an hours drive) because they were not going to hold up the bus to make sure latecomers got on. (now, I am 100% positive that they WOULD have kept the bus waiting, of course, to make sure all the kids were accounted for, but by 13 years old, it's not a bad idea to instill a little *personal responsibility" fear into a kid from time to time!)
Personally, I would let my kids go and wouldn't have a problem with it as long as the park allows 13 year olds to be there alone. I arm them with $500, $70/month-for-service phones for just such occasions! They aren't being dropped off in the middle of nowhere, they are at an amusement park completely within the reach of any parent if there is an emergency!