You don't spend much time on the Internet, I take it ... there's way too many people out there who would happily sell your death and dignity for a little bit of fame or money ... without a second thought what it would do to your family.
A compassionate person wouldn't consider making the video in the first place.
Ask yourself how many YouTube videos have been taken down because the person who posted them lacked either the compassion or common sense to understand why they shouldn't have been posted ... or they simply didn't care.
Would you feel the same way if the victim in that video was your kid or your mother?
... Bob (Grateful Diver)
You're changing the argument. The question of videotaping a rescue attempt can be challenged on a number of grounds.
First, is it legal? Second, does it impact the rescue? Third, is it morally appropriate?
With regard to it being legal, I believe that it generally is. Ther may be some locations where filming is prohibited. There may be some restrictions on what one can do with a video once made.
With regard to impacting the rescue, there are two possibilities there. One is that the photographer will actually get in the way while trying to film. Clearly, that can never be allowed to happen. The other is that potential rescuers would refuse to participate for fear of film being used against them. To me, that's an argument to fix the legal system more than a reason not to film. One might also argue that filming creates a situation where someone might create a secondary incident trying to stop the filming. Again, this can't be entirely laid at the feet of the photographer if filming is done from a distance that does not impact the rescue attempt.
The most difficult to resolve is the question of morality. Each person has their own moral compass, and that makes it more difficult. Things that are perfectly normal in one society might be out of the question in another. Personally, I don't find the taking of a picture or video to be morally inappropriate. I assure you that there are plenty of uses for that video that I would object to. There are probably a few that I would be okay with as well. If the victim survives and you didn't tape it, you can't reverse time and capture the event. If the victim passes, a responsible videographer could hit the delete button. You can argue that it will end up on Youtube, but that's not definitely the result. You ask what if the victim were a relative, but what if the photographer were a relative or close friend? I've seen a few videos of hairy situations shot by people close to a participant.
I would say that I am also a proponent of personal firearm ownership, or at least the right to own and carry. Many people are morally offended by the concept because of the potential for bad results, but I am okay with it. I'd like to see anyone who misuses their firearm punished severely, but they have a right to possess one. I think this is similar, conceptually, to how I feel about the video question.