It should be the mechanical crew to be honest. That is what they are paid to do. Granted I do believe that the OBS crew gets on in the yard at every point that I'm aware of. If I was working I would always top it off while in the yard reporting for duty but that is just me.
Enroute it is definitely the car attendant who is responsible.
I know the Star and Meteor the best but I know you can take water at WAS, RVR, SAV, JAX, I'm not sure further south because I haven't been south in a long time what is available but ORL rings a bell.
The Cardinal gets water at Russel, KY in a CSX yard by CSX car knockers.
The Crescent should be able to pull water in WAS, CLT, ATL, and I think BHM.
My other flight attendants get mad at me for always requesting our tanks be topped off everywhere we go if they are less than full but they also haven't been stuck in the New River Gorge without water for five hours either.
Now you are right that a few freight RRs have let the water hydrants go inop because a place like Hamlet used to have them.
As far as the distance between when you need water it depends on the passengers and the car type. A diner in real meal service uses a lot of water. And if everyone is taking showers you use a lot of water.