Disclaimer : I am not a lawyer biologist, please consider my interpretations with caution.
Note that plain water by itself wash a large amount of bacteria, especially when coupled with rubbing — and a shower usually lasts much longer than 15 s. There may be significant differences between the adhesion of bacteria tested in these studies and bacteria of the skin flora, though. (Or it may imply that antibacterial soaps only have a small effect, hence the mitigate results reported below.)
Anyway, Innate Immune System of Skin and Oral Mucosa (Nava Dayan & Philip W. Wertz, 2011) provides interesting informations on the effects of antibacterial soaps. I don't have access to the full book (and to its bibliography neither) but found the following extracts on google books.
The section
5.3 PROTECTIVE ROLE OF RESIDENT MICROFLORA
Contains a cautious consideration :
This protective role of normal flora suggests that an excessive use of antimicrobial skin cleansers because of not exhibiting a selective mode of action may make the skin vulnerable to infection by more hostile Gram-negative bacteria rather than protecting it [43-45].
The following section is of particular interest (I had only access to pages 96-97, though) :
5.6 EFFECTS OF SKIN-CLEANSING PRODUCTS ON SKIN MICROFLORA AND SKIN IMMUNITY
About skin flora population :
A comparative study on the effects of antibacterial deodorant soap containing triclocarban versus a plain soap on the skin flora found no significant difference in total colony counts [192]. However, more S. epidermidis was observed with plain soap, while washing with deodorant soap resulted in higher colonization of Acinetobacter calcoaceticus and Micrococcus luteus.
A latter sentence about another soap using the same antibacterial seems to contradict the above observation (maybe because of different settings or concentrations ?), though :
Both antibacterial soaps showed significant reductions in the skin flora
About microbiota regeneration :
These observations may indicate that mere washing of skin with plain or antibacterial soap does not disturb or alter the bacterial population in any significant way. Antimicrobials may cause reduction in the density of the skin flora for a short duration, and the skin flora tend to regrow to the previous level within 24-48 h.
About invasion of pathogenic bacteria :
There are also some misconceptions that regular use of antibacterial soap would lead to sterile condition and increase the risk of invasion by pathogenic organisms. […] [As of 2011] no evidence exists that the use of antimicrobial products may alter the ecology of resident skin bacteria that would lead to the overgrowth of pathogenic bacteria [185].
About resistance against antibiotics : [beware, likely outdated information, see DoctorWhom's comments — I'll edit with more details when I find some time to dig this topic]
Does the regular use of antibacterial soap by general population could lead [sic] to the emergence of resistant pathogens ? This issue has been widely debated in the scientific community [166-169]. [As of 2011] there has been no evidence of the development of cross-resistance to antibiotics due to the use of antibacterial wash products in the community [170-171].
Last but not least, I guess details are on a page I don't have access to but the authors state that
the use of antimicrobials may induce irritant and allergic contact dermatitis in some users
Finally, I guess this quote is a good summary of the state-of-art on the topic as of 2011 :
Clearly, more work would be needed to clearly understand the effect of long-term usage of antimicrobial-containing skin cleansers on skin microbiota.
However, the question is not about antibacterial soaps, but about antibacterial water. During a shower, soap is generally applied only for a few seconds on the skin before being rinsed. On the other hand, the skin is typically exposed to water during more or less 10 minutes, which is about 60 times longer. Assuming a similar antibacterial power, the effects of antibacterial water would be much larger than those of antibacterial soaps (all other things being equal, e.g. rubbing).
It would therefore probably be safer to avoid showering with such water.