Assuming that you flush it out for say 2 minutes, is there any problem with using a regular rubber or vinyl garden hose to get the water from an outside tap to fill your brewing pot?
The problem will be the taste. I have a guy in the homebrew club who uses a regular rubber hose, and will get some untainted brews from them, but after some period of time, everything will taste like rubber hose. He tried to change it out before it breaks down to that point, but there's no way to predict it, so he has had some bad batches here and there because of it.
I just use RV potable hose.