The captain is technically at fault, there can be no question about that.
This is what insurance is for, and what insurance companies are usually good at - the negotiation and resolution of a claim. Also, even a $5k settlement is less than pocket-change to an insurance company. But in some cases (eg high deductible) I appreciate that some would choose to settle separately. I myself would not agree to a settlement til there's an acceptable quote, and that an invoice copy is provided.
The city has acted like an a$$h0le, though. An inflated replacement cost, THEN not replacing the piling... that's pure BS.
Hope you're lovin' the great optics of this, St Augustine...