Perhaps we could let everybody have their own way by reading the Michigan Mushroom Hunters Club's take on the subject:
Let’s face it, mushrooms can be dirty… especially after a good rain. While we love the flavor of wild mushrooms, few of us like to eat dirt and bugs along with them, at least if we can avoid it. So, the question is what is the best way to clean them? Well, there really is no best way; there is only that way in which you are most comfortable.
Some people believe that you should never put your mushrooms under or into water to remove debris and bugs because it will reduce the mushroom’s flavor. Others believe that the bugs or even the soil found on or in the mushrooms can affect flavor, palatability, and a person’s health. You will have to make up your own mind regarding such things but it is a good rule of thumb to use as little water as possible when cleaning your mushrooms. (Click for the full article.) My bolding.