To be clear, Brad didn't refuse to have Cousins on the team. He replied 'no' when asked 'would you like to coach him'. There's a big difference between 'would you like to?' and 'will you?'. Remember that Brad, Danny, and the players hear lots of information that doesn't get out to the fans. IT played with Cousins in Sacramento, and hasn't exactly been beating a drum to get Cousins here, compared to how active he was with recruiting this summer. Who knows what information he gave to the Celtics leadership regarding Cousins' personality, coachability, locker room habits, etc. Likewise, Rondo played with him last year, and Brad may still talk to him as well.
With regard to the comments on BB and his willingness to take on problem players, most of those have been with regard to behaving badly off the field, not on it. As someone rightly pointed out regarding Jamie Collins, if BB doesn't like someone's attitude, he trades them away or cuts them right away. That's easier to do in football. If Danny brings Cousins to Boston and he tries to undermine Brad's system, they can either cut him and have his salary negatively impact their cap space for the next two years, or they can bench him and have the same problem, while still having his bad attitude around the other players. There is no good way to get rid of a malcontent player if they don't work out in the NBA.
Finally, Celtics management likely looked at whether picking Cousins up would make them good enough to get past Cleveland and into the finals this year, and what the impact would be going forward. In another malcontent move, his agent announced that he would not consider signing an extension wherever the Kings traded him to, so picking him up would be a short-term deal, and the player arrives with baggage from day 1. Given how good the current team chemistry seems to be, bringing in someone like Cousins seems pretty risky, for a relatively short term reward. If he was the final piece to win this year, maybe you take that chance. However, for the longer-term plan he really doesn't fit in, and risks slowing down or stopping the progress that has been made so quickly.