Maybe the idea is something like this:
Water cell(with bacteria and other impurity) --(electrolyze)--> Pure Oxygenated Water (Electrolyzed water cell) --(further process)--> Hydrogen+Oxygen..
or:
Water cell => cell containing some water, pressurized O2 and H2 (which can then be recombined in the cell to get energy + water cell) => cells just containing the O2 and H2