You are correct in that NASA ASRS is still available to you. VDRP is for the company only, not (you) the airman. When flying outside the US, 91.703 applies. You must comply with the rules of that "state" and ICAO Annex 2/SARPS.
The foreign version of the FAA (i.e. Transport Canada, DGAC, CAAC, etc) will be the entity that investigates PD's which occur in ICAO member states (foreign country). More than likely the case will be coordinated (through the state department) to the FAA IFO and/or your airline's FAA CMO.