Why no water
Mushrooms are absorbent — rinse them and they drink the water, then steam soggily in the pan instead of browning. Because ours are grown on clean substrate at the farm rather than in soil, there's no grit to wash off anyway.
What to do instead
Oyster mushrooms: tear the clusters apart with your hands and brush off any loose substrate with your fingers. Trim the very base of the cluster if it's tough — the rest of the stem is good eating.
Lion's Mane: brush the surface gently with a dry pastry brush or your fingertips. If you spot a bit of substrate clinging to the base, just trim that slice off.
Wild chestnuts: a quick wipe with a piece of dry kitchen paper is all they need.
If you really must
A barely damp cloth is the most water that should ever touch them — and pat dry before cooking. Then get the pan properly hot and cook them dry first: it's the single biggest upgrade to how mushrooms taste. More on that in How to Cook Lion's Mane.