Often insurance companies use a 3rd party valuation company. There are companies that specialize in valuations and insurance companies rely on them to get values.
Yes, you can likely negotiate the value; HOWEVER, the companies that do valuations support their values. Insurance companies wouldn't use them if they wouldn't hold up in court, meaning they have to have significant support of their values. That said, the way you get a higher value is to support a higher value.
Go on cycletrader.com, local newspapers and online resources and find as many similar motos to yours as you can. The closer to yours in mileage, age, farkles, etc the better it supports that value. Closer to your zip code also is better (values fluctuate over the state, nation). So, document your value in every way you can and submit it to your insurance company (or the other person's). One of the things this often does is show the owner the actual cash value (ACV) is lower than they thought; HOWEVER, I've also seen people's values raised based on good support and documentation. Document, document, document.