If you are trying to get car insurance quotes from a new company, they will check your credit, usually. They will quote higher rates to people with lower credit. That's kind of a standard thing with any kind of insurance, which is why they say a low credit score can cost you in other areas of your life. Your existing car insurance company isn't going to monitor your credit and adjust it accordingly, though. I've never heard of that happening.
i think this is spot on.
we had HORRIFIC credit scores in the early 2000's due to a series of events. our then insurance never changed other than the normal increases. we have worked to the point of having an 'excellent' score but it's yielded no benefits from the existing company (other than a great introductory bonus for getting their no fee/high (in some categories) rewards credit card).