Recommendations on this "water use" scenario

If your RV has a filter after the fresh water tank, I'd use the spring water, you can also add an inline filter before it comes into your tank, but I agree with 2oldman "It's your call. I've seen many 'non-potable' water sources which are just fine, it's just that the local water board doesn't treat it so it can't legally be called "safe". It may be just fine."
I too have drank (or drunk), water from many springs in my time nothing wrong with them, in several cases actually tested cleaner than some city water supplies,they simply were not over loaded with chlorine like most city systems, which actually tastes nasty.