Your second sentence is certainly correct. What we call a mushroom is the visible, flowering body of a fungal species. Fungi prefer to exist in damp, dark, and enclosed environments but the flowering body must expose itself to the atmosphere in order to effectively release its spores for reproduction. The reasons why it would be nearly impossible to remove all of the spores from the underside of a mushroom cap are twofold. First of all, the numbers are working against you. Spore producing species tend to produce large numbers of spores to increase the chances that more of them will ultimately produce new organisms. So you are looking at numbers of spores in the hundreds or even thousands. Second, these spores are tiny and look more like a powdery cloud when airborne so their dispersal is very effective. They are also buried within the folds of the gills under the cap called the lamellae, so you would have to search through much tissue to find these tiny spores.