FWIW I rinsed with untreated well water for years with nary a single bad batch to show for it.
Although I generally don't any more, I've done the same with no negative consequences. The this day, when I rack I sanitize the racking cane and tubing, then fill them with tap water from my well to get the siphon going. Nothing I'd recommend to anyone, but also never a problems doing that hundreds of times.
You run the tap water filled in the tubes into the keg? I'll usually run it out till the tube is filled with beer, then cap with my thumb, then run that into the keg.
As far as cleaning goes, using anything other than water on your kettles and mashtuns is overkill. I just rinse those buggers out make sure they look clean. Fermenters, however, they get the sh*t cleaned out of them. I make my own PBW with 70% Oxyclean and 30% TSP90.