A landmark settlement reached with New York State in 2009 required insurance companies to finance an objective database of doctors' fees that patients and insurers nationally could rely on. Gov. Andrew M. Cuomo, then the attorney general, said it would increase reimbursements by as much as 28 percent. Though the settlement required the companies to underwrite the new database with $95 million, it did not obligate them to use it. So by the time the database was finally up and running last year, the same companies, across the country, were rapidly shifting to another calculation method, based on Medicare rates, that usually reduces reimbursement substantially.