Since everyone is dancing around how Stoudamire was even on Batt's radar (most reports were pegging Richey or Kelsey), does make you wonder why they're being hushed about it.
IMO there are some possibilities, some more likely than others.
To me there is 0 doubt CDS was not only identified but also reached out to prior to Pastner being fired. The timing just makes that impossible to believe otherwise for me. There are some hire that seem like such a perfect fit that you could expect a quick turn around, but this isn't one of them. I don't think this is particularly damning or have any issue with it but you likely don't want to air that out nonetheless.
Now the next is pure speculation, but my guess is when Mazzulla was named permanent head coach, and maybe even prior, CDS started looking for opportunities elsewhere. It would make sense, Mazzulla wasn't some super proven head coach and was extremely young. On some level that had to hurt CDS to some degree especially if he had thought he might get the Arizona gig a few years back. Anyways, I doubt he reached out directly to J but my guess is he floated the idea of being the head coach to some of our alums and one of them reached out to J about it. Now, CDS wouldn't want that out there because being an NBA coach who is looking for a new job mid year, when your team is in such a good position, isn't a good look, and J wouldn't want it out there because after the circus that was our football search resulting in donors basically making the hire, he wouldn't want it to appear that this hire was anyone decision but his own even if it was just the identifying a candidate stage.