Based on what I heard from friends who were representatives from the T-6 and Unlimited classes and were involved with the situation, Red Bull wasn't interested in "sponsoring" anything beyond hitching their carriage to RARA's horse without really bringing much to the table at the time.
Obviously RBAR went on to develop, promote, and execute their own very interesting series of events without the assistance of RARA, but I doubt that any association or partnership with RARA at the time would have yielded anything beneficial to both parties. The motivations and interests of both parties and their spectator base were just too divergent. Interesting to note that of the two events, RBAR ran it's course first, and on a substantially shorter timeline.
Been going to Reno since I was a kid in the early 80s (with my dad, brother, and I having all been long-time spectators, crew members, pylon press members, etc.). IMO the apex of Reno was somewhere in the 1988 to 1991 timeframe. and has been on a slow incremental slide since then as the value of the unlimited racers skyrocketed and prize money slowly faded.
Even as late as the early '00s, it was still possible for an average dude to go out in the Biplane or F1 class, run in the Bronze class, and basically make the week pay for itself with the "average finisher" prize money. I crewed a Biplane class racer one year during that timeframe and was keeping tabs on the math to do it myself, and was in the purchase hunt for an S-1T to try and make it work. Alas, though, no more. Although there are lots of "everyman" racers in the Biplanes, F1, and Sport, all of those guys are footing the bill out of pocket.
There have certainly been bright spots on the downhill slide, and even an ember of new interest as Sport class has gained speed and spectatorship, but this is the inevitable termination leg of this particular journey.