You raise a fair question and you don't come off as a Hunt defender.A lot of people say this sort of thing and it confuses me a little bit, although I may be operating under some false assumptions.
I don't think anyone is under any obligation to hand over surveillance recordings to anyone else, right? If I'm running a luxury hotel I'm probably not going to show them to anyone but law enforcement. When people assert that the NFL had access to or could have accessed these recordings, do they mean legally or illegally? Do we expect the NFL to break the law to keep tabs on their employees' private lives on the off chance that they commit crimes?
I am also under the impression that you can't just fire people on suspicion that they have committed a crime, particularly when they haven't been arrested or charged or anything. Even if they fire someone for being arrested, are they not open to lawsuits in the event that the person is acquitted or the charges are dropped (not to mention this also being pretty unfair to people who've been falsely accused, even though that's not the case in this situation)?
Please don't take this as me defending Hunt's actions or anything, and believe me, I don't want to defend Goodell or any of the NFL owners, many of whom seem like terrible people. The NFL isn't God, though, and I think it's a little bit ridiculous to expect them to keep tabs on the private lives of every player and coach employed by NFL franchises.
To clarify, I dont know if the team or league attempted to obtain the video. However my take is that they had an inkling one or more videos of the incident existed and had a plan in place if it came to light. I could be mistaken but the quick release seems too tidy, especially for an organization that drafted and features Hill.
As for dcmissle's observation that lifetime bans aren't just, I agree. However the NFL, amongst other leagues, has a problem with domestic violence. There are reasons for that that are inherently related to the sport itself but regardless, its clear something needs to be done.
Banning a Hunt or Mixon or Rice for life may not be fair and this approach has its own set of problems (e.g. a spouse not speaking up about abuse for fear of negatively impacting their family's ability to pay the bills). However, the league's current approach isn't working at deterring any of this behavior and they have shown no signs that they are addressing domestic violence with anything other than cosmetic measures.