Help Me Understand Instant Car Insurance Quotes

I know there are a number of car insurance companies and comparison websites that offer a free instant car insurance quote but how can I be sure that they are accurate and true? How can I guarantee that they give me the quoted price? Why would a company give me the rate of another company for my convenience, even when the other companies rate is lower than theirs? I am skeptical of any company providing a quote of a number of car insurance agencies. I don’t know what one to use nor do I understand how it is possible for them to obtain these results. Please help me to understand.