It depends where in Canada you are.
In British Columbia, for instance, everyone has to have ICBC insurance. When a claim is made against your insurance, you always have the option to pay off the accident instead of it being an outstanding claim. So you can just let the insurance company handle it, and believe me they won't pay the highest estimate, they'll pay their own estimate, then pay it off once it's settled.
Interestingly enough, towing is included and doesn't factor in to what you pay the insurance company in the end. It's free!
Another note is you must be sure to pay the accident as soon as it's been settled with the insurance company, because if you have another accident, you will lose the option to pay off the first.
If you're not in BC .. Can't help.
