That is not a fact. Could happen, as some have confirmed, but depends on the insurance company, and your claim history. What is a fact is a collision with an animal is a COMPREHENSIVE claim, which automatically means NOT AT FAULT. So that's good. Unfortunately, for many insurance companies, a claim is a claim, so that may not mean much.Figure if you report it to your insurance company, you still have to pay the deductible and your rates will go up at least 15% for 3 - 5 years.
Having said that, I typically draw the line at twice my deductible of $1K, so 2 grand. And that's because I have a perfect record at the moment (no claims or tickets in the last 5 years). The good news is most insurance companies allow you to make a claim later, if there's more damage than previously thought... but talk to them first. Don't make a claim, but just ask if that scenario happens. Good luck brother. And hopefully a coyote being hit by another coyote will bring you good karma in the future. Ha ha.