Michael pretty much covers most of the bases, as usual.
As Michael correctly suggests, the entry forms were literally for entrants, not drivers. The entry forms for AAA events were standardized, whether it was the International Sweepstakes at the IMS covering 500 miles or a series of short events at the State Fair track at Hamline. While the format changed over the years, the paperwork for a sanctioned event was pretty consistent, for before and after the event. Not surprisingly, some promoters were better than other promoters and the same for the AAA representatives responsible for that sanction as well as the state and zone supervisors. Lots of paperwork floating around, in other words. Beginning with the 1910 season, under their new/revised rules, the Contest Board now required that drivers, mechanicians, and cars be registered each season. The same for tracks hosting sanctioned events. Yet more paperwork floating around.
For various and sundry reasons, not all of the paperwork made it to the mythical, magical, mysterious file cabinets lurking in the basement of the IMS Fall of Fame Museum. Keep in mind that this paperwork flowed from New York City to Washington, DC, to Indianapolis over a time span of eight decades by the time Gordon White managed to convince those at the IMS to allow him to microfilm the material. In more than a few instances, it was a pretty shoddy job in some instances -- pages out of focus, missing, only half a page recorded, and so on and so forth regarding the usual problems with any microfilming effort (yes, I am looking at you, Google Books....). I spoke with Gordon a number of times regarding this when we shared a table at the SAH annual meetings in Hershey. Gordon was primarily interested in the Midget material, that being his personal interest. He also told me that the microfilming effort apparently did not record everything in the file cabinets, those at the IMS literally pulling the plug for their own reasons. at any rate, those doing the microfilming halted at a point and that was that.
That Donald Davidson was not even aware of the Gordon White microfilm until I told him about it several years is not that much of a surprise, given that at the time it was being done Donald was actually working for USAC, not the IMS.
Until fairly recently, I think that it is safe to suggest that few now at the IMS had any real clue as to what may have actually lurked in the filing cabinets. The material was the purview of a very few and they tended to restrict access to it, especially "auto racing historians," for whatever reasons they had, but pilferage was certainly near the top if not at the top. It seems that when much of this material was at the AAA HQ in Washington, much it was "borrowed" -- a nice way of saying pilfered -- and never returned. The cock & bull story that Russ Catlin concocted is utter nonsense. Much of it simply appears to have walked off with someone. Never to be seen again, of course.
The AAA Contest Board material eventually wound up with USAC and then made its way to the IMS.
Along with numerous others, Jack Fox created and developed his material from a variety of sources, newspapers, programs, automotive journals, payout sheets, and whatnot, with perhaps some access to what was in the filing cabinets. As Michael suggests, Fox was not necessarily on target with what he had printed in his books and their revisions. If Michael seems a tad cynical, there are good and sufficient reasons for that. Fox was pretty much the one-eyed guy with cataracts in the land of the blind. Along with that of several others (I will not mention Russ Catlin, by name, of course), His Word became Holy Writ, and any confusion with facts contradicting some of that work being Heresy and Treason of the worst sort.
The likelihood of many of the early entry blanks surviving all this was slim to none, but a few somehow managed to do so. They are in the filing cabinets. But, they are quite few and nothing like complete. That Gordon White deliberately separated out the IMS material from the other AAA material did not help, of course. Basically, few really gave a sh*t about the non-IMS material, of course. In some ways that helped, but in others it did not.
Now, as for your theory, yes, doubtless that entry material and the sanction folders and ledgers were retained for a time, but, as they say, See Above.
Despite the efforts of Michael, John Glenn Printz, Ken McMaken, and others, there is still much to be done regarding the AAA era, Racing Board & Contest Board (not to mention the ACA, IMCA, and so forth). The usual focus on the cars and the personalities on the track and a very few events besides the IMS 500 mile events (Vanderbilt Cup & Gold Cup/Grand Prize) suggest how myopic, inept, ill-informed, and amateurish this has all been.
Michael tends to be cynical about the tech tables in the early US automotive journals, with good reason in some instances, but I still maintain that taken as a whole, that using the material to place things in context, there is much of value to be found in those journals. The use of the other archival sources and a good grounding in the era tends to lead to a very different impression of the era than most would realize. Again, not just singling out Michael but this applies to others as well, motor sport in the USA from 1895 to just the mid-50s is far more complex and nuanced and interesting (as in downright fascinating) than has been presented.
I could ramble on, but until we can entice those with scholarly backgrounds to begin to take an interest in this era, it will simply be the same old bullsh*t handed down and perpetuated forever.