If the pilot concerned does not trust his own company to do the investigation fairly and diligently, one option would be ensure that the relevant air safety board and airworthiness authority are aware of the incident (filing a service difficulty report, perhaps?). Having an independent third party doing the investigating would presumably quell any fears about the company biasing the investigation.
Of course, that only works if HE feels he didn't do anything wrong - otherwise its like calling the cops to report someone stole your drug stash...