He didn't trade Kyrie. He had left the team before that.
From everything Griffin says, and I truly believe it, LeBron does not give orders and is not the GM of his teams. Obviously, the presence of LeBron greatly influences a GM's decision making and the GM of his teams know that if he can surround LeBron with the right team, they should make the finals. It's a very unique circumstance that shouldn't necessarily discredit the fact that he did help LeBron win a championship and made the right decisions. He was able to surround LeBron with role players that fit a LeBron team very well such as Mozgov, Frye, JR and Shumpert.
Also, from what we have seen in Los Angeles this year - having LeBron is not necessarily guaranteed success. You still have to make the right moves like Griffin did to surround LeBron with a team he can have success with.
In addition to his time with Cleveland, I think it's very important to remember that he was with the Phoenix Suns for 17 years including 3 as the VP of basketball operations. Phoenix was often on the cutting edge of basketball innovations between their medical staff and style of play during that era. He should also have a strong relationship with Gentry given that he was the head coach during that time.
I don't think all of this means Griffin is necessarily the main target of the franchise - I don't think we should have one until we have interviewed candidates and I wouldn't be surprised if the GM we hire is someone we haven't heard of yet. But, I do think Griffin should be seriously considered and I think he would fit our needs greatly and I'd feel more confident with him making the calls than Demps and probably a lot of GMs out there. He's a very smart guy - just give him a listen on the BS Podcast:
https://www.youtube.com/watch?v=SMIklTBJG7Y