Both the concept and the motto pre-date Yeager et al by many years. It was primarily intended as part of a counter-ambush strategy ... the idea being that if a bunch of BGs had picked the place to ambush you, being somewhere else asap was probably a good idea. The enemy probably picked their location for maximum effect so getting out of that location lessens their advantage. Of course, if the goal of the ambush is to drive you into another even more dangerous location ...

From an individual "tactics" standpoint it's a bit different. Ken Hackathorn has done a lot of testing when it comes to the often-taught "take a step as you draw" thing, and last I spoke to him about it he still felt it added zero to your defensive capability. Basically, at handgun distances, moving two feet isn't likely to save you from a hail of bullets, a knife, or whatever.

On the other hand, if you can actually get away from the attack while delivering fight-stopping hits then do so. Making distance is a key to dealing with contact weapons (assuming you're beyond contact distance when the fight starts), for example. As rharris points out, it's a very natural ingrained reflex to get away from lethal danger. Contrary to popular belief, most untrained people do not stand still when being shot at. They move. Incorporating that natural response into your planned response might be a smart idea, then.

Furthermore, distance benefits the skilled shooter. If your opponent is just spraying & praying, the farther you get from him the more bullet-free space exists inside the funnel of random unpleasantness he's pointing at you. While we're all familiar with the KILOD numbers that officer deaths occur at a range of something like 5-10 feet on average, studies examining shootings in which officers prevailed tend to place the ranges much farther away. I don't have my notes in front of me but I remember learning at an IALEFI conference a few years back that when an officer is able to get 15yd away from his attacker, he's almost always the victor in a shootout.

So from my perspective:

Taking a step out of the way for the sake of moving one step: waste of time.

Initiating movement, moving toward cover, etc.: valid.