Are they pumping the water from the Muskegon River? No? OK... then... uh... what are you talking about?
No, most likely it does not. The watershed and the associated aquifer are where the river water comes from.
As to "what that assertion is based on", that would be "knowledge of how the hydrologic cycle works".
Yes, that's where it comes from, but it doesn't fill up instantly. Depending on the depth and type of aquifer the well is tapping, it could actually take a very long time for the aquifer to refill (or it could refill very quickly).
Are they widely used in places like Michigan, where there is plenty of precipitation? No.
Hint: nowhere.