I think it would depend on your header tank and distribution tank - "fresh" water is straight from the mains, but water from a bathroom tap has normally sat in a couple of tanks for some time in the loft or wherever. If these tanks are old or made of something unpleasant, or there are lead pipes in the system, you may not want to put the water in your tank.
As you can tell, I'm not a plumber or a chemist!