I think you kind of hear both because of the better safe than sorry and beer is robust camps. Both are fine, it's a personality thing I think.
Could you get an infection from your top off water if you don't sanitize? Probably. Is it common? No. There are lots of people who do it either of the two ways. Personally I spritz the top of the jug and cap area with star san to sanitize the part of the bottle that the water might flow over just like I do my yeast vials, but then I do not boil the water.