I do not know your cousin (his perspective is definitely well appreciated) but I know quite a few people in the Athletic Department and some of the donors as well. I have no idea what decision JW will take, but I can definitely confirm that JW really thinks highly of Groce, it is not a pretend or marketing like, it is a genuine very strong respect. Whitman has also been able to secure the support of some influential donors on his decisions (not just specific decisions).
This season is critical, but I am still not sure if Groce misses the dance, but makes the NIT, that Whitman will make change. I can't say that he won't, but I have some serious doubts. And before people start with the "NIT means nothing, nobody watches, etc." it has nothing to do with the value of NIT per se, but the fact that making the NIT means that Groce will be able to have a team that will be on the bubble, having a season around the .500 or slightly better. Combining that with Whitman's strong respect for Groce, I am just not sure he will make a change.
We may or may never find out... making the NIT is not a given at this point.
Based on the donors I've talked to, strong respect for JG is too strong of a statement to describe JW's disposition toward him. I'm sure he respects him, but I don't think he has a lot of confidence in him as the long-term HC. One donor said JW has been actively talking in back channels to prospective coaches about their interest in taking the UI job, including Cuonzo Martin, since the week he was hired as AD. He knows he has a lot of donors' support if he decides to find a new coach. He'd probably prefer that JG get the team to the Dance and remain as coach in order to save $$, but I'm guessing he's working back channels because he knows there's a good chance he'll have to make a change either at the end of this season or next season.
I imagine he wants UI BB to get back to becoming a perennial Dance team and B1G title contender and an occasional foray deep in the tournament and has to openly question whether JG can achieve that level of success based on his first 4 1/2 years on the job.