On top of demonstrating why the addition of a 3rd spoiling entity explains the behaviour through negotiations, I also have to demonstrate that it was the optimal strategy for all three not to reveal the presence of a spoiling external factor.
Well - as far as Israel is concerned, the Ministry went into great detail showing the links Saddam Hussein had with palestinian terrorists, while at the time of negotiations acted as if Arafat could have complete control over his terrorists. This spin was for the dual purposes of trying to engineer a war between various palestinian factions, and for the blaming of Arafat for failure of peace talks. Arafat, from his part all along said that guarantees on behalf of the various palestinian terrorist organisations were unrealistic even if the palestinian people in general would benefit from the results of the possibility of those said guarantees. As far as the third parties themselves, the whole point of supporting terrorists, especially suicide ones was that with the destruction of evidence during the actual attack there would be no effective evidentiary trail leading back to the original sponsor at the time. This is to be able to keep spouting anti-Israel rhetoric without anybody being able to prove or even define their links with said terrorists.