Years ago my brother worked for AP as newswriter in a major US city. He had so many stories about his bureau's photographer. He would famous for how sharp his elbows were, and that he would not just knock over an old lady, but one using in a wheelchair, to get the picture needed for a story.
So the issue is NOT just paparazzi. Successful straight news photographers have to be SOBs too. If you come back to the news office offer after saving a baby, but missing the assignment photo, or ever one minute later than the competition you are fired.
By the way this is not really First Amendment law. But mainly Fourth Amendment privacy law judicial precedence. In the US you have little expectation of privacy,, and under many court precedents essentially none if you are a public person. Unless a photographer bashed your head with their camera, or breaks into your private residence, photographing you, even on your private property is legal. Some very rich celebrities getting protective orders is about power rich people have in court system and not much else.
Also the alternatives are worse. CNN has been caught many times corralling "helping" people like demonstrators, and "re-shooting" a news event to make it look better attended/more newsworthy. To me that is a lot worse.
This film is compelling. And really to be honest people saying the photos should not have been taken are being dishonest. There is even science to back that up with people preferring to see these types of photos to any other news content.