It's probably not as black and white as the insurance company would like you to believe especially when they are looking out for their profits and not your interest.
If it had been me, I would have looked to see if my policy had an 'arbitration' clause to resolve disagreements. If it did, I would have refused the settlement offer and asked that for an outside mediator to settle the dispute. Most likely, the insurance company would do the math and provide you with a better offer just to avoid delays and the time and expense of going through the arbitration process
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