If the selection of the rating agency was assigned to a neutral party, like the Securities and Exchange Commission or the stock exchange on which the company is listed, then the agency would have no incentive to tilt its report in favor of the company.
It isn't on the table. But, while CEPR attributes this to special interest lobbying, I had never even heard the idea suggested by anyone, and wouldn't rule it out until it has had a fair hearing. The political world is not so intelligent and rational that it is aware of all possible solutions, and this may be one good idea that has a chance once put on the table.
Of course, SEC selection might prove distasteful to financial types who see socialism behind every corner, and privately owned and nearly monopolistic stock exchanges aren't immune to regulatory capture by their member companies. But, the idea would still be an improvement over the status quo.