From some comments I have read, it has dawned on me that many subscribers to archaeological discussion lists may not realize that the United States has decided to retain its "independent judgment" as to whether and to what extent the US will honor export controls of another country.
When you think of it though, it makes sense. Laws in other countries may be patently unfair or may not be the products of democratic compromise. In addition, foreign countries may not be using self-help measures to protect their own cultural property or may be requesting the US to impose import restrictions without seeking similar restrictions from other countries.
Below is an admittedly gross oversimplification of the applicable law. For more detail, I would suggest a close review of the State Department's International Cultural Property Protection website: http://exchanges.state.gov/culprop/overview.html
1. The 1970 UNESCO Convention allows foreign states to ask other signatories for help in enforcing their export control laws. The UNESCO Convention is not self-executing. In other words, signatories need to pass implementing legislation before the 1970 UNESCO Convention has any force.
2. The US only agreed to the 1970 UNESCO Convention with reservations. The reservations were intended to ensure that the US maintained its "independent judgment" as to the extent it would recognize another country's export controls.
3. Those reservations were embodied in the 1983 Convention on Cultural Property Implementation Act (CPIA). The CPIA set up an architecture whereby the US would exercise that independent judgement. Generally speaking, after a foreign signatory makes a request the US Cultural Property Advisory Committee makes recommendations as to the extent the US should honor the request and on what artifacts restrictions should be imposed. The decision maker in the State Department has generally accepted those recommendations. (An apparent exception was a recent controversial decision to impose import restrictions on coins of Cypriot types.) The US currently has restrictions on various artifacts from 12 state signatories to UNESCO. Most are poor nations that arguably need help in controlling their borders. The two exceptions are Italy and Cyprus, two wealthy EU members. The Iraq restrictions are a special case.
4. Before "regular" import restrictions are imposed (the findings for "emergency restrictions" are narrower), the decision maker in the State Department is required to make certain findings.
a. First, the restrictions can only be put on archaeological objects first found in the ground of the country seeking import restrictions that are "of cultural significance" or "important" ethnological objects.
b. Second, the decision maker must find that the cultural patrimony of the country requesting import restrictions is in jeopardy from pillage of archaeological or ethnological artifacts.
c. Third, the decision maker must find that the country requesting import restrictions is taking adequate self help measures.
d. Fourth, the decision maker must find that the restrictions are part of a "concerted international response" (on the theory that America only restrictions will only disadvantage Americans) and that less drastic remedies are not available.
e. Fifth, the decision maker must find that the restrictions are consistent with the interests of the international community in the interchange of cultural property among nations for scientific, cultural, and educational purposes.
5. There must be an effort to ensure that the import restrictions are applied only to the archaeological and ethnological material covered by the agreement and that fair notice is given to importers and other persons as to what material is subject to such restrictions.
In sum, while some vocal members of the archaeological discussion lists may want to honor the export controls of foreign countries in all circumstances, the applicable US law (which itself was the product of compromise) seeks to temper such views.