I doubt any of us really know whether Doc, Red, Phil, Pop are great coaches or whether their successes were more about great players. Red doesn't win 11 of 13 without Bill Russell and Phil doesn't win 12 rings without MJ, Shaq and Kobe. Etc.
I barely remember seeing Red on the sideline and I am 55, so I am dubious that any claim of Red's greatness is based on anything but hearsay. But with that said, Doc's work as a coach (like any coach), though recent, is only partially visible to the fan. In-game decisions and coaching philosophy you may judge, but practices, relationships, leadership, motivational capacity are factors (among others) that we as fans may make assumptions about, but we don't really know.
Red was probably an amazing coach, but seeing clips of a practice session and hearing soundbites doesn't prove it. And with Russell, Cousy, Hondo, Jones, Jones, Sharmin, Sanders, etc, there is reason to believe that the C's could have won with ML Carr at the helm. That said, I think Doc, Phil, Pop and Red are all good coaches with different skill sets, and at least two of them probably were great.
What seems undoubtable is the Red was a great GM, Phil made great career decisons, Pop got an incredibly fortuitous broken foot from his Admiral and the lucky roll of a ping-pong ball, and Doc made good use of two great trades by his GM.