A third party isn’t them though. I get what you are saying because LMG writes the check, but realistically that’s the best anyone can do. Why would the government get involved? Specifically why would taxpayers pay to help rehabilitate a private company’s reputation?
Private independent auditors are in every industry and a standard practice.
Oh, and as long as we’re being cynical, let’s say you got your wish and a government entity does the investigation. Odds are they would just contract it out to these same people. Same results, only everyone gets to charge more for their services.