Basically, you're getting scammed.
If you are not the responsible party, the other company is liable to pay for ALL your expenses. You don't have to pay your deductible.
With State Farm, Allstate, AAA, ect...
If you file a claim and choose to have repairs done prior to the other (at-fault) party's company claiming liability (fault), you pay your deductible. Subrogation then occurs to recover both the money your company paid out, AND your deductible for you.
Call them and tell them that the city claimed liability and that the claim is NOT against your collision coverage... making your collision deductible non-applicable. If they still give you grief, threaten to get a lawyer. It's probably not worth it to actually hire one for $500, but they are cheating you... they know it, and they might give in if they think you might pursue it legally.