Well since this is the Internet where we all spout wild-ass guesses about things I'll throw my 2 cents.
I think that SH and WM do care about athletics, and it is a priority (just not at the expense of APR). For SH, it's one of many priorities, for WM it's his main priority. Nothing too earth shattering there. I just don't subscribe our current place in the world to lack of caring.
From the SH perspective, I think she is smart enough to recognize that there is a direct correlation between Athletics and more money for UConn - something she has stated is a very big priority for her. People who have pride in their school are people that may donate back to that school, and for UConn, athletic success is a big part of that pride.
For WM, I don't think you need to be an alum to care about wanting to be the best. He played at Michigan, worked there- he knows what big time looks like, and that is the goal.
How to get there is the hard part.
Obviously both stepped in and were working with a real hand. Some things were beyond their control (and we debate endlessly where that line is).
What I think we, collectively as UConn have been guilty of, is hubris. I think it's been easy to sit back and say "we are great and our value is obvious" when that is not the case to those deciding our fate. If it was, we'd be in a better place by now. We are now in a place where pumping up our virtues publicly and constantly making googly eyes to the B1G or ACC stabs our new home in the back, but saying how much we like the AAC feels like giving up. It makes what SH and WM have to do that much harder (and keeps us all in the dark), because it has to be done privately now. And... Not having that visibility can be interpreted as not caring.
At least... I hope it's not lack of caring.