OK I guess we're heading right into the teeth of the issues thrown up by checks and balances of constitutional law. The executive has a foot in the world beyond the jurisdiction of the US courts. It makes treaties with foreign powers and must be seen to honour it's treaty obligations if it wants to make more treaties or expects observance of other countries' obligations. Extradition treaties have obvious advantages for both parties since, without them, criminals could escape justice simply by fleeing the jurisdiction.
On the other hand, the US guarantees it's citizens and residents fundamental constitutional rights of liberty, due process, freedom from arbitrary arrest etc. so there is a clear and obvious tension between two competing policy considerations. It is in the interests of US citizens to be free from unfair procedures but it is also in their interests to be protected from crime. Extradition arrangements serve the latter purpose by ensuring that fleeing the jurisdiction does not put miscreants beyond the reach of the law.
In our specific case, Amanda has been convicted in Italy. The US has a treaty with Italy which says in plain terms that extradition is a formality to be handled by the executive. The treaty confers no probable cause protection to persons convicted in Italy. It simply sets out the papers that need to be supplied. The question for an American judge from whom a person in Amanda's position seeks redress is: is the court concerned with the merits of the case against her or only with whether the (simple) formalities of extradition have been complied with? If the former, her constitutional rights are properly safeguarded but the US position in its relations with Italy and others is prejudiced and vice versa if the latter.
What we want is authority on how these tensions are being resolved in contemporary jurisprudence. I doubt we should expect to find clear and compelling authority either way.
