The treaty says:
ARTICLE VI
Non Bis in Idem
Extradition shall not be granted when the person sought has been convicted, acquitted or pardoned, or has served the sentence imposed, by the Requested Party for the same acts for which extradition is requested.
This is from a pdf of a letter from the US President:
Article 6 provides that extradition shall be denied when the person sought has been in jeopardy in the requested State for the same offense
It seems clear to me that 6 (six) is addressing a situation where the person has already been dealt with on the act that the requesting state (Italy) wants them for. If Amanda had been tried here that would be in force.
Now this is what Bassiouni wrote:
The 1983 U.S.–Italy Extradition Treaty states in article VI that extradition is not available in cases where the requested person has been acquitted or convicted of the “same acts” (in the English text) and the “same facts” (in the Italian text). Treaty interpretation needs to ascertain the intentions of the parties by relying on the plain language and meaning of the words. Italy’s law prohibiting ne bis in idem specifically uses the words stessi fatti, which are the same words used in the Italian version of article VI, meaning “same facts.” Because fatti, or “facts,” may include multiple acts, the Second Circuit Court of Appeals applied the test of “same conduct” in Sindona v. Grant, citing international extradition in US law and practice, based on this writer’s analysis.
Whatever the interpretation of article VI may be—“same act,” “same facts,” or the broader “same conduct”—Amanda Knox would not be extraditable to Italy should Italy seek her extradition because she was retried for the same acts, the same facts, and the same conduct. Her case was reviewed three times with different outcomes even though she was not actually tried three times. In light of the jurisprudence of the various circuits on this issue, it is unlikely that extradition would be granted.
He is clearly an expert, but what he says doesn't seem to line up with the text of the treaty at least in English.
It seems he confuses the treaty language with the Italian law. It seems so clear that Article 6 doesn't address double jeopardy in one country but rather in two. The treaty says you can't be extradited if you have already dealt with the issue in the country that is being requested to extradite.
As for the our rights not applying abroad, I don't think they are a red herring but you may say that.
The Italians certainly could argue that since the US will try a person twice on the same facts even if found not guilty the first time that their three level system is no more a violation of DJ.