I think that came down to intangibles -- and if Cook didn't have red flags on his personality and leadership ability, he would have been off the board long before the Patriots' pick.
I read a lot of things like this on Cook:
Connor Cook Leave Some Teams Uneasy in NFL Draft
Representative quotes from scouts and coaches in that article: "“There’s something about him that you just don’t trust him.” "there’s something missing with him.” “There’s just something put-offish about him." "he’d be a guy that, when he got in the locker room, they’d try to eat him up and spit him out."
At some positions a "something off" personality might work out ok. But at quarterback?
Meanwhile,
Jacoby Brissett:
"Highly competitive and ultra-tough." "senior captain with natural leadership qualities – sent his offensive teammates hand-written notes before every game and baked desserts for his offensive line…self-motivated with insatiable work ethic" "Good football-playing temperament. Takes the game seriously with good football and personal character."