I found this study on iodine that says that in a petre dish, iodine does NOT have antifungal properties, but in the body it does. Possibly due to immune modulating effects.
Perhaps, it is this mechanism that purifies water.
"When topical, iodide acts as a disinfectant and an antiseptic.4 The ability of potassium iodide to directly destroy microorganisms continues to be speculated. Although the pharmacological literature states that potassium iodide has no antifungal activity in vitro, a study shows that cell lysis occurs when Sporothrix schenckii yeast is exposed to increasing concentrations of the drug through the release of lysosomal enzymes.4,9 Also, considering the immunological action of iodide in vivo, it is possible that it has some direct effect on the infectious agent. However, more studies are needed to confirm these mechanisms of action."