No reason to force someone on Gase if that's who he wants. Same goes true for Rhule. If that's who you want, then you have to trust him to hire his own guys. Otherwise he isn't your best candidate. I think there's a lot we don't know about how the hiring process went down.
I'm thinking as part of the interview process they asked each coach who they wanted as part of their staff. With Rhule, maybe they didn't like who he wanted as his staff and decided that the total package of Gase as HC and playcaller was better than Rhule and who he wanted as his OC. Essentially Gase is his own OC. Sounds like his choice of staff is what dropped him below Gase. Not necessarily that Gase himself was the better hire. From what I've read, Rhule was not actually offered the job.
I guess they trusted Gase to hire his own guys more since he had NFL experience. Maybe the guy Rhule wanted was a pile of excrement. No evidence on who it was other than "an NFL offensive assistant"