The courts ruled on the DJ thing with the Mexican case and maybe more. Clearly the Italian type system doesn't work with the 5th unless we accept that the trial isn't over and no verdict is assigned until completion.
here's some stuff from a recent article - just more stuff
The only legal argument that Knox, her lawyers, and other advocates have made thus far is that she should be protected by America’s commitment to preventing double jeopardy. They claim that Article VI of the U.S. extradition treaty with Italy incorporates the American meaning of double jeopardy. But the Article only relieves the U.S. of its obligation to extradite if the subject is charged with the same crime at home. Even if the Double Jeopardy Clause of the Constitution were in question, it would offer Knox scant hope.
The Fifth Amendment states, “nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb.” It sought to prevent the “unacceptably high risk that the Government, with its vastly superior resources, might wear down the defendant so that ‘even though innocent he may be found guilty.’” That means preventing the government from retrying the same person for the same crime if it doesn’t like the result it gets the first time around.
What’s happening to Knox isn’t the type of legal abuse that the Constitution sought to prevent. Knox is trying to dodge the consequences of an appeal, not a new trial after the conclusion of a legal process. As Reuters reported of the Italian justice system, “No judgment is considered final until appeals have been exhausted.” What happened is what can always happen: “[T]he top Court of Cassation can order a retrial which adds years more to the process.” (So far as inapplicable constitutional arguments go, Knox might be better served ditching the Fifth Amendment for the Sixth, protecting the right to a speedy trial.)