I think it's not really the ability to type fast, or that you need to be typing all the time, but that when you're in a state of flow, where you have what you want to accomplish and put down on paper/screen clearly in mind, a context switch, even as one as small as from keyboard to mouse, might be slightly hurtful to that state.
When I'm in this state, I'm probably writing pseudo-code fairly close to the real language I'm working in, and not worrying too much about errors I'm not seeing, and just trying to quickly correct the errors I do see, such that I can express my intent on screen. Finding missed typos and other errors is for a second pass and with the help of a compiler/interpreter, for code I write in that manner. It may require some additional passes to tweak things that just don't work, as well, but that's fine. The point was to get what was very clearly in my mind transferred to another medium before something caused a corruption of my mental state.
That's not to say that's the only way I write. I also often devote time to carefully pondering what's on the screen and how to best interact with it to change it in the way I want, or whether there is a better way to do it entirely and that code should be rewritten. But when I'm trying to get what's in my mind onto the screen, little things like auto-indent and being able to accomplish something while keeping my hands doing what they've been doing all add up to help in small ways.