There are two main types of mange - (forgive my spelling) scarcoptic and demodectic. Both are caused by an air breathing mite that can only survive on the skin.
As the mite cannot live underwater on fish scales it is unlikely that dogs could catch it from swimming with fish!
As the mite cannot be transferred by saliva or through the stomach it cannot be caught by eating fish.
All dogs (and humans) have mites on their skin it is just the type and amount that differs. They are ugly tick like looking bugs that can only be seen under a microscope after a skin scraping. The mite is transferred by skin to skin contact. I found three 8 day old pups in a packet. they were covered with scarcoptic mange. Because of all the handling of them I contracted mange (scabies) aswell. It was not fun but fortunately easily treated and resolved.
You can confidently tell you friend that fish will not give dogs mange even if they swim with them.
