Many things are under copyright such as images, music, written papers, patents, etc. For the amusement parks that means that their logo, name, taglines, etc. that sets their company (including ride names) apart and is their trademark are protected.
When I went on the Busch Gardens behind the scenes coaster tour, they asked us not to take pictures of blueprints. This protects coaster designers like B&M, Rocky Mountain Construction, Vekoma, etc. from people copying and using their designs. I believe that those ideas that are unique to the architects and designers should in fact be protected.
However, when we are talking about the actual ride itself, everyone can have instant access to the ride once you pay park admission. This then brings up the question of why on ride filming is not allowed. Some might say they want to protect their "intellectual property" ie. roller coaster designs. Many places that I've been to reserve the right to allow filming while you are on their property, which extends past amusement parks and into regular businesses. Some places such as sports arenas, carnival grounds, etc. may also not allow filming, because again it is their property.
The bottom line why most parks don't allow any type of filming is not just because of safety, but because of copyright. They are in the business to make money and reserve the right to allow/not allow their guests to take pictures. The park can do whatever they want in regards to filming and do not need to ask for your written permission when filming. By entering the park you agree to comply with their rules, regulations, and submit to having your picture used for marketing, etc. It also may be easier for a park to say that on ride filming is a safety concern, because that's something the general public would understand, but it's really more to it than safety.
I personally believe that amusement parks should share their rides with their guests by allowing them to film their memories while on them. Amusement parks are in the tourist industry and tourists want to share their videos and pictures of their experiences. Busch Gardens and SeaWorld have done it right and Busch Gardens Williamsburg even has behind the scenes access for their rides, while most parks do not even offer this.
It is my hope and dream that amusement parks around the world would allow GoPros and other types of action cameras for on ride filming and not be selfish when meeting their guests needs. There needs to be a way that there can be a compromise of allowing their guests to film. Perhaps they could have a camera fee that guests could pay, which would allow them to film on the rides. Most families would not be able to afford something like this, but for those that want to film while on rides, they would be able to do so.
Below is a link that discuses more in detail about copyright within the amusement ride industry.
