The First Amendment of the Constitution of the United States gives *anyone* the right to record *any* situation in the public especially if it is the interest of the public. You don't need a permit from the government and you don't need permission from the government. You can use your eyeballs, a camera, or a drone as long as you follow the existing laws and that includes NOT flying under a TFR. I believe there is a rule about interfering as well.
There is no such thing as the *news* in this context since everyone has the capacity regardless if you work for the tv station, the local newspapers, or you have a press badge or not; doesn't matter. When I check the drone rules, I see nothing about needing a part 107, crossing over traffic, maintaining 100 feet, vehicle location, and as a recreational pilot, nothing in part 107, etc. Just follow the rules like you would do every other day of the week and you are fine. Just because you pull out a drone doesn't mean you now fall under some special authority or special circumstance. Until someone comes up with a workable process, this is all we have to go with. "Leave the area and don't come back" won't work and anybody who depends on that is not helping IMO.
At this point, that's all you need to worry about and maybe one day the authorities will figure out how to safely integrate such drone activities into the situation instead of trying to eliminate them which is a non-starter. The same was said and tried with news helicopters, the same can be done with drones as well. If for some reason it cannot be figured out, I have some ideas.
My comments apply only to the hypothetical situation that was brought up in the OP; nothing else is implied or inferred.