I don't see how you can get anything from THEIR insurance company. Since you are not their customer, I would be surprised if they even talked to you. You will need to submit the claim (however high the bill was, all of it was your expense) on your homeowners insurance and then let professionals at your insurance company recover whatever costs they can from your utility, which (if successful) will then subsequently go on THEIR business insurance.
Even though there is nothing wrong with your logic, nobody ever parts with their money unless absolutely necessary, least of all public utilities, some of which have 100+ years of experience dealing with issues like yours. Depending on how high your deductible is, it may not even be worth submitting a claim, but you are the only one who can judge if it's worth it.
Good luck!