Sometimes scientists will go through all of the data from previously published studies from different journals (called a meta-analysis) to try to get an overall picture of results from the different studies. In one such meta-analysis from 59 different articles on Azospriillum (Azos) they looked at the effects of Azos on wheat growth.
When it comes to beneficial bacteria and fungi, I have 2nd hand knowledge (but from very reputable sources) that some of the mykos on the market is about is worthless as kitty litter. I know the grower that sent samples into labs, contacted the distributors and in some cases the problems were corrected and in other cases they were not. So when it comes to beneficial bacteria and fungi know the source and know the expiration date because sometimes what is on the label isn't accurate and in other cases what is in the bag is largely dead and not viable.
So back to the studies.
In looking at the value of Azos and its effect on wheat the conclusion was that "A mean increase of 8.9% in seed yield and 17.8% in above ground dry weight was found to result from inoculation of wheat with Azospirillum." Now I know that pumpkin growers aren't growing wheat but you won't find 59 studies on Atlantic Giant pumpkins (more money in wheat) so you have to extrapolate. But if I could get a pumpkin 8.9% bigger by using Azos I'd do it every time.
As I understand it Azos has an affinity for grasses, so the effects on cucurbits might not be the same. I can't find any studies done on cucurbits, but I can give the observations from my own experience and a few other growers. About the time that Azos became commonly available on the marketplace myself and three other growers applied azos to pumpkin seeds when they went into the pot. All of the growers saw the same thing. Faster and aggressive germination. As near as I can recall I all saw the same thing. Each of us lost one cot leaf because it was tore off as the seed popped from the seed shell. It could have just been a coincidence, but it seemed to common for it to be just that. Because of that, I put my Azos about half way down in the pot so it doesn't come in contact with the roots immediately.
For is this myth busted? I don't think so. The data seems to suggest that Azos can possibly produce bigger pumpkins.