On Food Channel Alton Brown's show Good Eats and also Gourmet.com (7/2008, p. 36) question: do mushrooms get soggy if washed?
Mushrooms are 90% water. Mushrooms don't soak up much water when washed.
You should dry on paper for 15 minutes if you wash them.
Some cooks like to brush them or towel them. Watering them is okay. You choose.