It makes more sense to me in performance driving. You can only go around a curve so fast. What matters for your overall time is coming *out* of that curve under control, so you can hit the gas hard and go fast again. The rule of driving is to go just slowly enough on the slow parts to go faster on the fast parts. In that case, it is a hard and fast rule - if you hit the corner too fast, you *will* be slower overall. The mindset is that you can never gain time - you can only lose it.
I think that's what it's really trying to say with regard to shooting... but there aren't as clearly defined "fast" and "slow" parts. To me it means a "slow part" would be "make sure you have a good grip" or "make sure your gun doesn't have to go above the target and come back down on your draw," or "see your target and your sights." All of these things require you to slow down from the fastest you could be doing the actions in order to reduce your extra movement and be in a good position to hammer on the fast parts.
If you hit the corner too fast, everything else will be slow. If you draw the gun faster than you can actually acquire a proper grip and see your sights, everything else will be slow.
It was never supposed to have meant "go slowly all the time."