That depends on how you define cautious. One person's cautious in another's smothering. If you cannot let a 15 year old out of your sight at Disney, one of the safest large public venues to do so, then how can you expect them to function in a few short years when they are hundreds of miles form home on their own? My 13 year old went to Disney on a school trip this year, on her own. She and a group of friends toured together, with mandatory check ins twice a day. They had a great time.
I teach high school. I have watched parents so terrified of what's lurking around every corner cripple their kids to the point they cannot function at college, they end up coming home to live with mom where she can monitor. They NEED to be allowed to do things away from mom and dad before they are thrown out on their own. Being so scared of the HIGHLY unlikely chance they would be abducted/ assaulted at a theme park that you won't let them visit on their own falls into that category. A 15 year old is a high school sophomore. They will soon be driving themselves. At what point are they allowed out of parent's sight? Does the 16 year old get to drive themselves to the store, or could something bad happen? Everyone wants to say, "I'm not that bad" or "but that's different", but is it really? Smothering is smothering.