At an aircarrier, part 121 or 135 or other certificated holder, an ASAP program can and should come as part of an MOU, Memorandum of Understanding. Most union carriers address non sole source reporting at this stage.
At my company we had a real fight over this but the company wanted ASAP as part of a overall insurance reduction program, so they were willing, as was the FAA to accept that non-sole-source reports would be exempt from discipline or certificate action. This was with the PROVISION that the incident in question was not specifically exempt, ie. Careless Reckless, criminal or drug or alcohol related. The event in question would still have to pass the event review committee which is one union, one company, one FAA.
To date, to my knowledge, we have not had any ASAP non sole source reports result in FAA or company discipline or certificate action.