Pierre, with the greatest respect, not all parties are equally willing. In fact, some parties will be quite reluctant to engage in any process, whether it's mediation, conciliation or anything resembling a meeting of minds. However, their willingness to engage might well be enhanced if in fact the CORE, the ombudsperson, had the ability—and that ability was lurking in the background—to say “we can compel both documents and testimony”.
In fact, you have described a variety of situations where the evidence will be extraterritorial. I agree. It will be sometimes less than optimum. I agree. Why would we allow a process to develop that will be necessarily less than optimum in a situation that will always—always—be extraterritorial and be fraught with difficulties and conflicts?