In sports, players asking to be traded is pretty common. It's unheard of that a team immediately trades a player on request, they usually try to negotiate with the agent for a year+, and only trade them as a last resort if their play on the field suffers or if they're bringing down the rest of the team. When a player requests a trade, it plummets their trade value to other teams and because Hernandez was in the 1st year of a huge contract, the Patriots would have had to eat most of that contract. Most teams and agents assume that a trade request is about playing time, more money, a better fit in the playing scheme, etc......... not about a secretive double-life the player is involved in.
Also as the documentary says, Hernandez had a firewall between his criminal personal life and his life in the NFL, where players, coaches, and owners thought he was an example of how the NFL can rescue a troubled player from a situation like this. For Hernandez, it was the opposite. The area of complicity between the Patriots and Hernandez was with his "Weed house" the secretive apartment that they got him where he smoked weed all day... which, sure, that's a bad look, but the team being complicit in a player smoking weed is far from involvement in murder, especially in Massachusetts where marijuana use is not as stigmatized as much as other places in the country.
Beyond that, though, it's not like trading him would have cut off communication to some of the people he was involved with. One of the attempted murders was in Florida with the alleged witness of the double-homicide outside the Boston nightclub. Troubled followed where Hernandez went, in Connecticut, Massachusetts, and Florida.