why are water fountains by the bathroom?!

They have water fountains near the closest water line. And actually, all the water is clean. Even the water that goes into the toilet, it is all filtered through a system. The only thing that makes toilet water gross is the actual germs that go into the toilet. And yeah, the bathroom sink water is the exact same thing as the fountain water, only difference is it is usually cold. But the bathroom sinks usually have options to have cold or hot water.

You are correct.

When I install a toilet, I always make sure the waste water is connected to the fresh water line near a fountain. Just to give it some taste in case the fresh water has gone 'skunky'.
;-)

Bert the plumber.

THey are there because that's where the water line already is. Do you really think they take the water from the toilet? Wow.