In the past for jazz draft picks it was always a collaboration when it came to picks. Jerry Sloan had an influence, koc/scott layden had an influence, Larry h Miller had an influence, and a few others as well.
Idk if it is still that way but there is a chance that DL liked trey a little and maybe liked someone else a little more but the coaches, owner, and other jazz management felt strongly that the jazz should pick trey burke if they could and DL went along with.
When it comes down to it DL's name gets stamped on every pick, trade, free agent pickup that occurs but that does not mean that he always goes with what he thinks is the best thing to do. There are probably times when he thinks plan A and plan B are both good plans but he favors plan A a little more than plan B yet still goes with plan B due to the influence of others involved in the decision making process.
The jazz are run like a democracy where everyone has a voice. It's not a monarchy like some other franchises
That is absolutely the way both the Jazz and DL operate and DL confirmed this in numerous interviews. Anyone who listens to DL's interview during the Big Show on the Zone during draft times (which I did quite a bit) would also know this.
DL also said this is what they did when he was with the Spurs and it's why they've been so successful.