If they truly believed in his ability, they would have promised him more game time, promised him a place in the CL squad and given him a salary fitting his reputation and they would have kept him.
I believe (based on actual statements made by Sarri, agents and other Juve officials) that Juventus wanted rid of Kean all along (along with Higuain and Dybala who they couldn't sell) to fund other transfers - namely Lukaku / Icardi. Kean waited as long as he could for another team with European Football to make a serious offer, one wasn't forthcoming so (with days left in the window) he came to us.
You appear to believe that Brands went over there and bullied Juve into accepting a low-ball offer with no buy-back clause, for a player they were desperate to keep and Kean rejected loads of other top teams to come to us.
Nobody knows the real reasons he left Juventus, one can only guess. But your version of events doesn't appear likely to me.
Can you post the statements where Sarri says he's wants rid of Kean. I've had a good look and can't find anything.