Blackmail is a little strong. I think it's more that foreign countries wouldn't say anything publically as it would admit to them harbouring terrorists, or worse, that they are incapable capturing them on their own.
Also, US isn't the only country that does rendition. The Brits and the Germans have sent Spec Ops into the Balkans to capture war criminals to bring to the tribunal years after Balkan conflict. The Israeli's did the same thing to find Nazi War criminals in places like Buenos Aires
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