They do not have to look to the future they could have their world-class CIA level security team dig into the player and see what type of people he is associating with. Hernandez was dancing on tables at Rumor Tuesday with a gun in his waistband, do not pretend that he was at church, and took a wrong turn all of a sudden. Ignorance is not an acceptable excuse.
Needless to say you have ignored every other poor decision and decided to focus solely on the one that you could somewhat excuse. I am not bashing Belichick because I do not like him, heck he is one of my all-time idols but his decision making in recent years has been suspect.
1. You're dramatically overstating the level of information that the Pats have available to them. CIA-level? They talk to his past coaches, his family if they can, and maybe some old acquaintances if possible. Beyond that, what do they have access to beyond the standard background check? They'll look more deeply into his background than your employer will into yours, simply because of the money involved, but it's not like they have access to his web history and a comprehensive list of all known acquaintances. The bottom line is that the Pats have no idea what most of their players are doing most of the time that they're outside the facility, and that's typically not a problem. That's life as an employer.
2. Look at the number of players in the NFL who have arrests relating to gun possession and/or assault on their records. It's a huge number, and every single one of them has more red flags re: his capacity to commit violent crimes than Hernandez did at the time of the murder.
I know it's tempting to assume that there were warning signs indicating that he was a deranged lunatic, but look at the facts. His record consisted of a rough upbringing, possible juvenile gang affiliations from his juvenile years, and a couple of failed pot tests in college. Yeah, that puts him more at-risk than someone like Tom Brady or Jerod Mayo, but let's be realistic. How many NFL players fall into the exact same risk categories? A ton.
It's an uncomfortable truth, but it is what it is. Any criteria by which the Pats could have been reasonably expected to foresee this also disqualifies a ton of other players that the Pats could really use, and 99% of the time it doesn't make a difference. Have you ever advocated that the Pats sign a player who's been arrested for a violent crime? I know that I have, and if you have as well, then there's really no grounds on which to say that they should have predicted that Hernandez, with no real warning signs, would turn out to be the guy that he is.