I have always washed mushrooms and in fact...
.... it's a pet peeve of mine this huge misconception that gets spread everywhere from cookbooks to magazines to forums that mushrooms are sponges and get soaked with water if washed
nonsense! They do not absorb water at all - if you weigh them, soak them for 20 minutes in water, rinse them and weigh again, there's no gain!
Mushrooms have a ton of grit glued to them, the delicate brushing with a wet paper towel does nothing to really clean them, and is a major pain in the "derriere"
My mushrooms take a nice shower, with a nice massage and then are prepped for cooking, I dry them lightly on a paper towel, that's about it.
I don't know why some mythgs just stick and are almost impossible to get rid of ;0))))