This is just a guess, but even when you're doing something as simple as changing the battery on your car, you need to register the battery. Either the dealer does this or you can do it yourself by purchasing a bavarian technic cable and running a command.
A guess could be that when a new water pump is installed, some kind of command (or several) must be run in order for the car to recognize the new pump. Talk to a mechanic at the BMW dealer and ask if they do in fact need to do this extra step to make it work, and then ask the indy shop if they have done this after they did the physical labor. Or the other way around, whichever you prefer.