It seems like bond rating services here are an obvious point of comparison. They got paid to rate bonds, which meant they got paid by people with a strong desire for certain ratings, which meant that they "competed" not on price but on laxity of ratings. Most of us know how that one played out ~8 year ago.

Independent investigation is great, but you're right to observe that "outside" is not necessarily "independent". I suppose there are a few solutions to that: you could break the financial link (in the bond case, get consumers or the government to pay raters), or you could establish a culture where inaccurate results destroy reputation.

I'm sure there are auditors who do objective work for the people paying them simply because they value being known as reliable (and who are hired because the auditee wants a result people will trust). Without some precedent, we probably shouldn't assume that rosy case is happening.