Distilled water is condensed evaporation, not water that has sat around for a while waiting for substances to evaporate from it. The modern method of chlorinating water usually doesn't use a volatile (can evaporate) type of chlorination, so letting water sit does not remove it. This piece of advice comes from a time when the chemical used to chlorinate water was a type that evaporated quickly.
There can also be fluoride and/or lime in tap water, neither of which are appreciated by many plants, or evaporate within a short amount of time (days.) There is no way to remove these things from water except through filtration designed to do specifically that. Distilled, caught rain water, the condensate from a dehumidifier, are good sources of water without these chemicals added. Bottled water may or may not be tap water from somewhere, may or may not contain fluoride, chlorine, balanced PH, etc... If it's ground water, like from a spring, it's going to have some minerals in it, which won't be visible or mentioned on the label. Plants may or may not like them. I wouldn't use this expensive and 'unreliable' water for plants.
