We don't know. But we have read all the same reports and this is what looks like happened.
Pegulas take over team, spend record amount of money. They call Polian according to reports to help them evaluate the football operations.
Marrone leaves.
Polian declines Czar position.
Pegulas now ask Doug Whaley, the guy who was on the chopping block just a week ago to prepare a list of ALL coaches as the Bills were to do an exhaustive search. They interviewed a crap load of candidates. Almost every major coordinator and head coach out there.
Pegulas use the interviews to build intelligence on their new toy and to get plans on how to fix Bills.
Rex gets interview and wins the interview. Wows everyone, especially the new owners who want to impress fans used to settling for cheap, unwanted candidates.
Rex is hired and Whaley signs off.