Having worked within self-certification systems albeit in a different Industry the one think I can say is that self-certification only works if the leadership and guiding mind(s) within the Organisation are committed to it.
When profit and or especially salary is related to performance then the relevant documentation will always exist in the system. I have known this to happen when overloaded Managers did not have sufficient time to exercise due diligence and documents were signed and submitted to confirm that those checks HAD been undertaken. This was to maintain performance levels against which the Managers and their future career opportunities were measured.
Only truly independent audit, with auditors paid bonuses for finding failures will resolve the situation.
Sorry if this appears cynical, but its called experience and old age.