I started out shooting a bow when I wasn't much more than a toddler by pinching the arrow between my thumb and forefinger, floating anchor and eyeballing down the shaft. That was how my grampa taught me and, a few years later, it was how my Comanche friends shot their bows. Killed mucho small game and wild pigs that way. Imagine my chagrin when I took an archery class in college and found out I'd been shooting all wrong.
Isn't this also known as an "Oriental Grip"? I don't feel there is a "right" way to shoot a bow, to be perfectly honest. I think it's whatever feels comfortable. I learned with the "one on top, two underneath" method myself, but have seen MANY people using three under or two fingers split. I've seen a lot of differences in stance and anchor points over the years too. I used to shoot a recurve just like I shot a compound. Then I was "taught" to: lean forward, cant the bow to the right (I'm right-handed), draw and sight at the same time, and the second your index finger touches the corner of your mouth... release. But it didn't feel right to me. The leaning forward bit seemed to take away some of the arrow speed for some reason. I started standing upright and shooting "normal" (normal for me) and I got improved accuracy and better arrow speed. Admittedly, I'm no expert like most of the guys on here, but I feel it's all a matter of what feels natural and most comfortable.