I have found that for the most part, parks really don't care that much. I have had a video of the Under the Sea number from Voyage of the Little Mermaid for the last two years with nothing happening.
One of my favorite youtube-rs out there is Bribery, a Disneyland Cast Member on the Storybook Boats. When not being a cast member, she stalks many of the characters and has ongoing discussions with them. They are actually very entertaining and show the talents of some of the actors. She has had a couple of ride videos too. I have yet to see any yanked videos. So check out Bribery!
I think you start getting in murky waters with the shows because of the talent and music. One example I can think of is the Flower Power Shows such as Tony Orlando(a must see when he comes to EPCCOT!) which probably is no good!
Still, youtube is free and TPI is free to use!
My thoughts are not until the park is portrayed in a negative light or there is a major safety issue. It's interesting to read about the paps following celebs. The parks are private property, but purchasing a ticket gains them entrance, but they must adhere to the guidelines of the park.
I've dealt with paparazzi on film sets on the streets of Los Angeles. Under those "controlled" circumstances there is a give and take between them and the production and ultimately both parties get what they need and leave each other alone. But I cannot imagine having to deal with them inside a park. Their running around in public to get there $$$$$ shot without regard to the people around them is what really irritates me. Sadly, the only real way to stop this is buy not reading/viewing the tabloids. (I could go on about this topic, but I will stop here)
But why wouldn't parks want people to post photos and videos online? The majority of it is good free press. I tip my hat to TPI for not allowing videos on the site that are against safety regulations.
Eventually it comes down to enforcement. If parks start doing this, they can't pick and choose, they have to sue everyone. But, I feel there are better rules like line-cutting that should be enforced.
Oh, and on photography on rides? Some outdoor rides are fine to photograph, but the rides with dark elements are forbidden! I can imagine 50 cameras from an Argentinean youth herd or Brazilian tour group flash during Spaceship Earth - patooie!