We use our onboard water supply at need, without reservation. And we always keep some water onboard, in case of need (planned or not). If the water source was safe to drink to begin with, we have no compunction about using it weeks or even a few months later. I do, however, like to refresh the tank every 6-8 weeks if we have not been using it. It tastes better, for one thing. My wife drinks a lot of water and mostly uses bottled because of the consistent taste. She only buys certain brands because of taste differences. But she still uses tap water when convenient, and for cooking, coffee, etc. unless it is really strange tasting (e.g. sulfurous or highly alkaline)
One of the reasons for the dichotomy on this subject is that our digestive systems are highly adaptable. If you regularly drink from different water sources, or water that may be less than 100% pure, your body deals with both the chemical differences and any microbes it may contain. If you don't, your body loses that ability over time and becomes susceptible to differences in the water. Mexicans don't get Montezuma's Revenge - they drink their water every day. For the visiting gringos, the results are often different!