It really sounds like there is nothing to worry about using straight tap water as top-off water. But when I think about using straight tap water (not boiling and cooling it) the angel pops up on my shoulder and says, 'If it isn't broke, don't fix it'.......then the devil on the other shoulder says.....'Don't listen to him, you're wasting your time and money boiling and cooling.'
I think the devil is right here, but I'd hate to end up with a batch that isn't as good b/c of the lack of a chlorine boil off or whatever, or even worse a bad batch, but it sounds like that's not really a concern.