I did some digging as that article from CR didn't give any reference as to that recommendation. It seems that it is preferable to use only water on the wound itself and a mild soap around the outside of the wound. However the water needs to be free of any contaminants, there are references to using either distilled water or saline solution to clean the wound (the CDC says saline is preferred otherwise use bottled water - Ref:
Emergency Wound Care|Natural Disasters and Severe Weather ).
It also seems that the use of hydrogen peroxide to clean wounds is fairly controversial with no clear winner as to the use/don't use sides, but with a lot of websites claiming it should not be used but giving no reference to a source to back that claim up. I looked at a few websites that gave a little more information, it seems that in addition to killing off bacteria it might also harm skin cells which can result in wounds taking longer to heal or leaving a scar. However, and this is where the controversy seems to come in, there is not yet a clear indication of weather this is an immediate result or the result of multiple, repeated, applications of hydrogen peroxide to the open wound. Here is one study in which this is challenged:
Hydrogen Peroxide: A Potential Wound Therapeutic Target
Sorry to derail the thread and for the headache you will soon have if you start down this rabbit hole of research!