If Budenholzer was requiring McD to give up some of his power, you can be damn sure that was discussed. Suns said no, Bud withdrew. That seems just as likely, maybe even more so, than Sarver lowballing him.
Think about the timeline (what little we know of it). Bud meets with McD and the front office team for 2 days. Then he gets on the phone for a 1-on-1 with Sarver (who was apparently with scouts in Europe watching Doncic at the time). He withdraws after that. It could be that it was this 1-on-1 call where he demanded more control that he couldn't really demand when meeting with the very guy he would take that control from. Sarver showed loyalty to McD and said no, Bud withdrew consideration.
I don't know if that's what happened, but it doesn't seem far-fetched.