Why is this so hard for you to believe?
I believe it. But I think the reason people resist so much is that nobody's been able to identify what makes the difference. Clearly, some people simply rack on top of the sugar and have been doing so for years and years and years and have never had a problem. And just as clearly, at least a handful of people have had consistent problems doing it that way, which went away as soon as they started stirring.
I do not believe it is "magic", there must be some factor that is different, whether it's process, ingredients, equipment, or hell maybe even something esoteric like water chemistry or elevation or ambient temperature at bottling time or what have you.
I work as a software engineer on the controllers for high speed printers. A few years ago, I was working on uncovering some weird timing bug -- things that are timing related can happen randomly, or can sometimes be triggered by just weird unrelated things because it changes the timing of something else. There was a tech who could reproduce the bug every 20-30 minutes or so. I carefully watched exactly what he did, and then tried to replicate it exactly, even stupid apparently irrelevant stuff like opening and closing the paper tray at a particular time. I tried for hours and hours to reproduce the bug with no luck. We called the tech back in, and he made it happen in 5 minutes. I had him watch my process, and he couldn't spot any differences either. And yet, even when I tried again, no luck.
Nothing magical was going on here, clearly there was just something subtle he was doing differently that neither of us could spot. I eventually narrowed down the bug -- unfortunately it didn't shed any light on this mystery, since like I said it was just some timing issue; it could have been triggered by anything.
I gotta believe something similar is going on here, since different people are reporting such consistent (and yet divergent) results. It's a mystery as to what is going on though... all the usual bases have been covered, and yet still a handful of people report bad carbonation if they don't stir. Go figure.