John,
Probably too site specific to discuss, but yes, in general, no trees is better. I have seen a few situations where planting a willow helps a bit in drying out soil, but because they are trash trees, you would never want to plant them too close to greens, tees, or fairways where they would block shots, etc.
Besides, French drains probably are a better wet soil solution (or surface drains) than the willows. And, come to think of it, how many times have we seen willows or other water loving trees break through pipes and clog them in search of water?
Lastly, water loving trees tend to be shallow rooted, causing the same problem Sergio faced at Medinah (yes, he was upland) so they can break wrists, mowers, etc.