I gave both my ds's cooled boiled tap water until they were about 12mo (ds#1) probably younger with ds#2 & then stopped boiling it (both were bf, so I felt pretty comfortable with that)... I drink our tap water (unboiled)
I think it depends on where you live, where I live the tap water is considered totally drinkable as is, so boiled is fine... I know other places it isn't so palatable / has high mineral content, so different recommendations apply, but if you drink your tap water then it should be fine.