I do not think it is video that is the issue, it is the fact that a drone was used. The use of drones inside a national park is illegal without special permission or permits. Many state parks also prohibit drone use. This is one of the first lessons (or should be) for a drone pilot to learn. I live very close to a national park and videos of wildlife and other scenic views are often taken and posted. And, as you mentioned nearly eveyone has a video camera (cellphone) with them and are taking videos of everything that moves. However, fly a drone in the park and you will most likely get a stiff fine and your drone confiscated.

As a Part 107 drone pilot certificate holder, I can say that the subject of prohibited and restricted airspace is rigorously taught. Prohibited airspace is taken seriously by federal, state, and local governments. Much of the airspace above us is controlled or restricted in some manner.

Of course, many people buy and fly drones without any training or thoughts of where they can fly them. This is a huge problem.

The issue of taking videos of police and other public service employees is another issue. More and more government agencies are looking at restricting photography of their employees.