The credit bureaus, now more formally known as consumer reporting agencies, are separate businesses. Each markets its services to lenders and consumers. While you're right, it's more common now for your credit history to be reported to all three agencies, that's no reason for two of the agencies to get out of the business.
FICO is a separate company that provides the models for the consumer reporting agencies to create independent credit scores. As you point out, it also markets its own credit score.
Insurance companies have been using credit scores as an input in pricing auto and homeowners insurance policies for years. The fight has been fought over whether it's legal for them to do so, and the insurance industry won that fight. However, there are limitations on how an insurance company can use the information in your credit report in pricing a policy.
The Comprehensive Loss Underwriting Exchange is an insurance claims history database that allows insurance companies to access consumer claims information when an insurance company is underwriting or rating an insurance policy.
A report from the database includes policy information such as the name, date of birth, policy number, claims information such as date of loss, type of loss and amounts paid, and a description of the property covered. For homeowners insurance, the report includes the property address, and for auto insurance, it includes the specific vehicle information.
Under the Fair Credit Reporting Act, you have the right to request a free copy of your report from the claims history database annually. Your ability to dispute information in the report also is spelled out in the Fair Credit Reporting Act, and it uses the same dispute process as credit report disputes.