It is all about the starting ENERGY.
Not only speed but geometry and timing. You don't need to be as fast as the plane you're trying to catch, only be at the right place at the right time for a killer solution. You don't need to follow the exact same zoom timing and geometry as a 262, not when you can delay your zoom up and take a "shortcut" to where you've got a solution from.
Also a nitpick: when flying fast enough, bullets will be slow enough in your frame of ref that they're moving like slow motion. It might be possible to fly fast enough and fire slow enough rounds that they're too slow to hit their target.
do any of those twisty turny floppy maneuvers in a 109 and i guarantee you end up as a greasy spot on the ground...
Let's see some film instead of vague anecdote.
some of us try not to do the strange fishy stuff, while others live by nothing but gaming the game...
irrelevant to whether or not the hitech quote in your post is accurate.