Quite honestly it's not the factor you having a secured camera at all. There are no trade secrets or privacy issues. The bottom line is that if you have a camera then they now have eyes that can post to the internet any neglect or accidents that may occur at the park. It just may happen your camera catches that one day when a car goes off the track. They then won't have control over that camera because they don't own it. So the "easiest" way out is to ban them all together. Regardless if it's secure or not. You can claim safety and you would be right. That secure GoPro attached to your chest via four straps is a liability issue to the park.
It goes along with filming police doing their jobs. Look at all the videos of out of control police. To stop or slow that the police claim it's for their safety and you are interfering. I say always question authority. Always ask for where the law is stated or the manual at a park that says no cameras. I've had instances where my answer was it was what I was told and I'm just passing it along. Very few cases where the employee would show me any memo or page in a manual stating no cameras.