I don't know if it is true that both parties should share responsibilities of any parking lot accident. But one thing is sure: DON'T TRUST THE INSURANCE COMPANY. They will do whatever it takes to reduce their cost. To find out for sure, check with your insurance company and ask for advice. Some insurance companies are nice to their own clients. Every insurance company has its attorney team. Sometimes they will deal with the other insurance comapny on your behalf. You can also try some law firms which offer free first time consultation. But I guess they will not be interested in your case, since it does not involve too much money. If you feel sure you deserve 100% compensation after doing your research, call the insurance company and threaten to get lawyer involved, or to take the case to the court, better business bureau, etc. In most cases they will not insist since for them it doesn't worth it to spend too much effort on small cases. They end up spending more than saving any.
Good luck.