I think it's the same thing, since once you're doing a rolling stoppie, physics says you're at the point of maximum decceleration - it's just a force balance. If you instantly grab a handful, you might lock the front tire or you might flip the bike, so you have to ramp up the brake pressure - but this happens very quickly, and it's only during this brief moment that the rear brake is of any use. My point was just that trying to use the rear brake during this brief moment is a distraction from your main task, which is lofting that rolling stoppie as quickly as you can.
It's been a while since I've done stoppies, since the BMW just doesn't like to lift the rear wheel. But, back when I was playing around with them, I found that they didn't require as much of my attention as would be expected.
I think your model of motorcycle dynamics is overly simplistic. For instance: applying the brakes not only compresses the forks, but also creates downward momentum at the front of the bike. It's the job of the shocks to control this momentum, but they don't do so perfectly. It's very plausible that applying the brakes extremely quickly will cause the front suspension to compress
further than it would if applying the brakes gently. I don't think I need to make a case for why greater fork compression would increase the tendency to stoppie.
As another argument is that, compression of the front forks creates an easily observable pitching movement around the center of gravity of the bike -- inertia. A stoppie is also a pitching movement, centered over the front wheel. It's very likely that the initial pitching momentum around the CG would reduce the amount of braking force needed to lift the rear wheel (just another motion.)
As a counter example, some riders are known to yank up on the handlebars in order to begin a wheelie. While I'm not sure this is an accepted practice, it's easy to see why it would work. Yanking on the handlebars creates a backwards pitching movement that should help lift the rear tire.
I'd argue that it's possible that rear wheel braking creates a backwards pitching motion, that would actually work against the bike's tendency to go over the front wheel. Remember that engine braking, especially when combined with rear wheel braking, creates a squatting effect.
So, there's three good arguments showing that the rider's control actions may have a noticeable influence on the motorcycle's tendency to lift the rear wheel.
Counter question... If the rider shifted his weight onto the back wheel (perhaps by sliding back on the seat,) how would that effect braking and stoppie behavior?
In my estimation, it would make bike harder to stoppie -- the rider would have to apply noticeably more front brake in order to lift that rear wheel. Would applying more front brake before the wheel lifts mean shorter stopping distances?
