Each state has its own laws or statutes that govern insurance companies. Most states have a department of insurance (DOI) or insurance regulator as part of the state government agencies to help consumers understand their rights, obtain needed insurance for things such as motor vehicles or file a complaint if necessary.
Insurance department sometimes give the direct information you need on their websites. For example, Florida's DOI site states that according to Florida statute 627.7282 when you have been quoted one price for automobile insurance but received a policy for a higher premium rate you can: pay the increase, request cancellation or do not pay and let the company cancel your policy for non-payment.
Most insurance regulatory bodies understand that the discrepancy in a quote compare to the actual premium rate can be because of information that was revealed by your motor vehicle record or other researched information that required the original rates to be changed. These agencies do urge consumers to get an explanation for the increase and encourage those that feel the first quote was intentionally low to obtain a person's business to file a complaint.