I'm not out to defend certain questionable members of the press here, but I'm not at all convinced that they'd like to get their hands on a "shocker" video. Can't speak for other parts of the world but UK news TV (which would be the only real medium for video coverage) is pretty strict about what it shows when flesh-and-blood people are involved. Even showing dead bodies after a massacre or battle is considered a borderline subject.
Personally I think the real threat comes from individuals on forums such as this one -- a quick click on the Internet would allow anyone see video footage with virtually no accountability.
I've been quite disgusted by the Airliners.net spotters who thought it would be "educational" to put the broadcast tape of a (ironically) news reporter's fatal helicopter accident on their forum.