I think the most damning evidence against the idea of pulling up is the average graphs which show that the faster group of riders pull up almost not at all on average. But, as Fday has pointed out, the difference in pedaling technique doesn't seem like a statistically significant difference, for the statistical reasons he cited, and for the less sophisticated reason that, "hey look, the hardest pushers were roughly middle of the pack for speed, and the fastest guy pulled pretty hard."
The impression I'm getting from this discussion is that pushing down isn't inherently better than pulling up, and that pulling up might be better than pushing down. But I don't think we've established that pulling up is important enough to focus on in coaching sessions.
Looking at the two groups, one group being state level riders, the other being national level, we see a variety of pedalling techniques.
If pedalling technique was vital to cycling success, then I can only assume that we would probably see all of the pros using essentially the same technique.
Since we don't see that, I think it's a logical assumption to make that pedalling technique is not all that important.
Maybe we should consider the possible biomechanical advantages of pulling up. Citing the popular cyclist mantra, cycling is not a strength limited sport, so we shouldn't expect the extra strength contribution of the hamstrings and hip flexors to make any difference.
Since strength doesn't make the difference, the benefit would have to be from increased aerobic efficiency. My understanding of aerobic efficiency is that it's basically limited by how much of the oxygen you breath can be consumed by your working muscles, which is restricted by the surface area of the blood vessels in the muscles, which is a function of muscle volume and vascularity or capillarity or some physio term like that.
Adding the new muscle groups involved in the pulling motion increases the muscle volume, probably substantially. This means more of the oxygen you breath in can be involved in power-generating processes, which means more power and faster riding.
I imagine the reason why this doesn't make that much of a difference, is that your glutes and quads are large enough muscle groups that they can already pretty effectively drain your blood of oxygen.
And now, anyone who actually knows what they're talking about is welcome to tear apart everything I've said