About 15,000 dog bite incidents a year by police K9's against officers or bystanders and a little under 200 incidents of a lost K9 officer indicates that even your exception isn't one. A dog off a leash can bolt or attack anyone, no matter how well trained. The difference training will make is if they come back to your side after they spit the person or creature out. Keep your dogs on leashes.
I made my comment about K9’s because I worked with them in the military. In the 3+ yrs I did so none of the dogs in my Squad or any other I was aware of (United Kingdom) were involved in instances as you describe.
This does not mean some fools were not bitten who believed they could pet the “nice doggie”. That did happen and those bitten were themselves in the military but like the man said, “you can’t fix stupid”.