My guess is that he was really confident that he'd endear himself to White if he went dicks out to try to get him that job and that he believed the probability of White actually landing it wasn't all that high. The best thing for Rhule to keep White (or anyone on staff who is good) is to show them that he truly wants them to move up in the coaching world and he will do whatever it takes to help them get the right job. Pushing for the UCLA job shows White that if Rhule thinks it's a great opportunity he will push for him and that will hopefully mean that White will be selective in the opportunities he pursues