Old-school (British and European) cooking gurus such as Delia Smith, Gordon Ramsay, the Larousse Gastronomique
– all say don't wash, but the hip young guns including the scientifically-minded food writer Harold McGee and his disciple Heston Blumenthal say it's nonsense. Give them a good rinse, they say.
Some people say that mushrooms are like sponges and soak up water and will be ruined if you rinse them. Harold McGee wrote about this in his New York Times column 25 years ago. He did experiments and concluded that briefly rinsing mushrooms is unlikely to make much difference at all.
I have always rinsed as I don't like cooked soil in my my mouth, but that might just be a baseless phobia. I don't care. I rinse mushrooms.
Do you use water when you brush them? I'd consider that washing or maybe scrubbing. I usually wash them in water and then kind of rub the outer layer off. Kind a like scrubbing but with my hands.
Maybe I will use a brush next time - like I do with potatoes.
This is what I do. With potatoes as well (with then I use hot water)