I Googled for comments about the Aunt Becky. Some said that it's really important to use the right kind of thimble with it. This thimble is sold on Jean brown's website but you have to kind of hunt for it. From what I can figure out, this is the type of thimble that has a deep indentation on the top -- sort of a rim around the top. Someone who watched a demo said that the end of the needle is held inside this indentation, near the rim edge, and the thumb holds it there.
Again, from what I can tell, the needle is held stationary this way while the underneath finger moves the fabric onto the needle. I watched a video that demonstrated how Jinny Beyer hand-pieces, and it is a similar technique in that she holds the needle stationery and manipulates the fabric onto the needle for the stitches. She is amazingly fast at doing this!
I think that, even once you understand the theory behind each technique, it can take quite a bit of practice to get good at it. The advantage is that it's a lot faster. I have seen knitting techniques that are similar -- where the knitter manipulates the yarn onto the needles instead of moving the needles -- and again, that is much faster than our traditional methods.