Aeromonas hydrophila, some scary stuff. I've read that povidone in a wound won't take care of the bacteria, chlorhexidine even has problems. Can't say what would happen to the girl if she was iodinated, but it reads like it was a very deep cut.
A lot of fish heal miraculously in the ocean, it's the salinity I bet.
Can't have Iodine alone though, throw in the co-nutrients like Selenium and Magnesium that are in short supply.