Is it true that very high quality water (ultra pure) can actually
deteriorate into unhealthy contaminated water through storage?

Yes, that is true fact. Ultra pure water is the perfect solvent. Presently many reef tank owners use R/O [nanofiltration], Ion-exchange resins and combination sof R/O + mixed bed resins or split bed resins + mixed bed resins producing high quality water [conductivity: 1.0µ/S-0.243µ/S] which requires the addition of buffers and minerals supplements before it can be used during replacement water changes. If this water is to bused as replacement for evaporation many add calcium, magnesium, iodide, selenium, and trace elements solutions. However, the big problem for reef tanks is the hobbyists lack of knowledge of high quality water's unique solvent effects. First, high quality, water should have conductivity measured via gold flow cell, on an instrument capable of reading to 0.056µ/S, calibrated by a prepared 25µ/S standard solution. Second, all ultra pure water must be piped sealed through teflon or polypropylene tubing/pipe into a sealed polypropylene storage container. All pipes and storage tanks must be flushed with ultra-pure rated water prior to first usage. If any air contact is made this highly reactive water will be turned into literally waste water. For example: 1.0-2.43 µ/S water will absorb plastizers, VOCs, heavy metals out of most plastics and then absorb any room's undesirable gasses CO, CO2, NH3, O3, N2, VOC's which then produces [5-100µ/S] gas and impurity saturated water. This water will contain: vinyl chloride monomer, epoxides, cyanides, thiocyanides, heavy metals, volatile amines, trihalomethanes, other volatile organic chemicals + CO2 Gas, NH3 Gas & other atmospheric gasseous contaminates. This contaminated water is then dosed with calcium, strontium, selenium, iodide and assorted trace elements before addition to the reef tank. This R/O or D.I. water may also contain heterotrophic bacteria or endotoxins that grew in the filter media. Ref.: Heterotrophic menace: fact or fiction?, Water Technology, Feb. 1999. Utlra Pure water is not considered potable water by the U.S.E.P.A.