Now, we have access to independent video in a relatively small and unsystematic sample of those cases; and it turns out to differ from the official story fairly frequently.
But are these videos widespread because they exist, or because of the disparity between stories?
How can you ask if these videos are widespread when the OP is pretty much telling a few lines above that the videos represent (and I quote) "a relatively small and unsystematic sample of those cases"?
There is no reason to believe (nor data to back the belief) that people are filming only when a cop shots/hurts someone just upload them when the cop is in the wrong (and not uploading them the cop is in the right.)
So, without evidence that filming folks are displaying such a bias, then we have to consider the films as a really good random sample (of a small size, but it still random) out of a larger population of events (police encounters ending in confrontation, officially described "justified" on average.)
So now that we take a random sample (the videos), and we see that the expected properties ("justified on average") doesn't hold, then we have to re-examine the basic premise (that "justified" might not hold as common as it is officially trumpeted.)
Obviously, more evidence, more films (larger, more representative samples) are needed. But that doesn't deny the troublesome picture these films portray.
And to be honest, we all know this shit has been going on forever. We just like to pretend this shit doesn't happen, that them folk got it coming, and that the entire American experience is (and was) a mix of The Andy Griffith Show, Leave It To Beaver and Lassie.
It takes a couple of death people caught on film to get that shit of a notion a second look, doesn't it. That speaks volumes about a society's infinite capacity of self-deception.
Are there videos that show justified shootings that don't make national news because there's no story other than "cop defends life of self and/or others"?
Are you trying to prove a negative?