There's flat, and then there's FLAT.
On a gentle site with 1% to 2% fall everywhere, you could build a pretty good golf course without moving earth around, as with Paul's example and many other old courses.
But if the site really has 0% fall, like The Rawls Course, and it's not very sandy to the point you can trust the water will drain down, then you have to contour pretty much the whole site to get the water to go somewhere. It's ridiculously expensive to re-grade 200 acres, 80-90% of which will never see a ball land on it, but nobody likes to see puddles in the roughs, either.