I don't water my Trachy much. Just during extended dry periods. What I notice, growthwise, is that my Trachy grows fast in spring (April, May, first half of June) and fall (October, early November). And, it seems to respond instantly, in a good way, to soaking rains during those months. So, in my experience, I wouldn't say Trachies dislike water, but maybe they dislike tap water. There is a difference. Many plants will take tap water if no other kind is available, but they don't love it. My tap water is drawn from underground aquifers and has a very high mineral content. Add to this that our water mains are old and rusting. So, there's a bit of rust in the water too, which I believe is iron. While iron is essential to healthy plants, it's unwelcome in moderate to high concentrations.
As for Sabals, yes, you can't drown them.