When something happens, the real cause of the problem is often due to a combination of the entity (the company/person/whatever that had the "something" happen), as well as external factors. Those external factors can include rules/guidance—or the lack of rules/guidance—from multiple agencies.

If a regulatory agency is also doing investigations, they may choose to focus less on their own 'failings' (that is, their agency's rules/guidance or lack of rules/guidance), and focus more on others' failings. Or, they may choose to focus less on other agencies' failings for political reasons.

Having a third party, with no regulatory ability, helps to reduce the appearance of bias, and increase trust in the industry that the third party investigates.