The neighbor is right, you need to go through the insurance. He clearly is looking at the situation realistically and handling it properly. I am sure he is aware of the consequences of going through his insurance and the possibility that they may demand something be done by the dog, but it is the correct way to deal with the situation. The claim should be through his insurance - I THINK (I'm a little unclear on the exact details here - it sounds like because the dog didn't actually attack you, your foot was maybe just "collateral damage" and you don't say if he actually did any injuries to your dog - I'm not sure where the line is draw on things like this with insurance). You need to notify your insurance company of the incident no matter what, though.
Yes, you are right, the loose dog was actually after my dog. He made no attempt to bite me or my daughter. Unfortunately, I sustained this injury while trying to separate the two dogs. My DH said that was my mistake. I should not have gotten in between them. The thing is, the dog attacked from behind. I did not know he scaled my fence until he was upon me and my dog.
You should not lie about trying to "catch" a dog though, or try to make the incident into something other than what it was. You should be completely clear and truthful about everything that did and didn't happen. You do not want to be caught in insurance fraud. (Also, saying you were trying to catch a dog might shift the burden to your insurance since that makes it sounds like the dog was not a threat.)
Definitely do not want trouble with the insurance company. Just want to do the right thing while trying to spare this dog. I don't blame the dog as much as I do for owners who were not responsible for training their dog long ago. To them, a huge lesson learned.
While it would be sad to have to rehome the dog, or deal with higher insurance rates/insurance cancellation, that's a choice the neighbor made when taking the dog in in the first place and not properly training and/or restraining him. It's just one of those things in life that as adults we make choices on, and we get to live with the consequences on. As I often say, "It sucks to be an adult". But we deal with it, hopefully learn a little in the process, and move on.