Tom,
I'm sure I have found a green site and worked backward occasionally. The 7th at the Quarry comes to mind.
I would probably have done more of that if I had been offered more spectacular sites, which I think tend to demand that a bit more. If I found a nice-looking green site with a tree on the north side, it would become pretty obvious that the hole would have to play from the E, S, or W of that tree.
As to hazards, design is more of a circular process. As Mike says, if there is a really unique feature you might start from almost anywhere, and work one way, but the design is never done until you work it backward to make sure everything really works as your first impression may have told you. Most often, for me, the land around the green site wasn't particularly spectacular, but most often it made sense to put the hazard on the low side of the green as a natural fit. Then you can work out the rest.
But overall, I think it most often makes sense to find a tee location (which should be near the previous green, of course) and work it out as a golfer plays it. We can say that it isn't always a myth, but it is one of those pithy sayings that has gotten far more play than the supposed process underlying it. Hey, it does sound like it makes sense, lol, and as you say, sometimes it does.
Mike,
Certainly, as a player, you are likely to judge it by where you play. I think it is the job of the architect to anticipate how all players might reasonably play a hole. Judging a design on your own game has also led to some less than desirable outcomes, i.e., JN and his greens bent hard right to fit his game, CB Mac routing all holes hooking out of bounds because of his slice, etc.