Well maybe...

I know he wasn't arrested by the FBI, however, for example, the FBI claims full jurisdiction to arrest as long as the person is on US soil.

http://www.fbi.gov/about-us/faqs

>What authority do FBI special agents have to make arrests in the United States, its territories, or on foreign soil?

>In the U.S. and its territories, FBI special agents may make arrests for any federal offense committed in their presence or when they have reasonable grounds to believe that the person to be arrested has committed, or is committing, a felony violation of U.S. laws. On foreign soil, FBI special agents generally do not have authority to make arrests except in certain cases where, with the consent of the host country, Congress has granted the FBI extraterritorial jurisdiction.

http://en.wikipedia.org/wiki/Extraterritorial_jurisdiction

>Criminal codes in certain countries assert jurisdiction over crimes committed outside the country:

>in France, the Code pénal asserts general jurisdiction over crimes by, or against, the country's citizens, no matter where they may have occurred.[1]

>in Japan, the Penal Code specifies certain cases and applicable lists of crimes over which jurisdiction will be asserted.[2]

>The ability of Parliaments of Commonwealth countries to legislate extraterritorially was confirmed by s. 3 of the Statute of Westminster 1931.[12]

>In Australia, extraterritorial jurisdiction of the State Parliaments was authorized by s.2 of the Australia Act 1986.[13]

>The Criminal Code of Canada asserts jurisdiction over the following offences outside Canada:[14]

>on a Canadian aircraft in flight, or on any other flight which terminates in Canada, for any indictable offence

>on any aircraft or in any airport in the world, for endangering such facilities

>by a Canadian citizen, permanent resident, or stateless person resident in Canada, for offences relating to cultural property protected by the Hague Convention for the Protection of Cultural Property in the Event of Armed Conflict

>against or on board a Canadian ship on the high seas or a fixed platform attached to the continental shelf of Canada, or by or against a Canadian citizen on any ship or fixed platform, or by any person who is found in Canada after such offence

>on a Canadian ship or aircraft, relating to hostage taking, offences against internationally protected persons or United Nations personnel, or terrorism financing

>on the International Space Station involving nuclear material involving terrorism terrorist activity against Canadian citizens or Canadian government missions, or intended to compel the Canadian government, or any provincial government, to do or not do a particular act relating to sexual offences against children

>In the U.S., many states have laws or even constitutional provisions which permit cities to make certain decisions about the land beyond the town's incorporated limits.

>The US Criminal Code asserts the following items to fall within the special maritime and territorial jurisdiction of the United States, much of which is extraterritorial in nature:[19]

>The high seas and any other waters within the admiralty and maritime jurisdiction of the United States and out of the jurisdiction of any particular State, including any vessels owned by US persons that are travelling on them[20]

>Any US vessel travelling on the Great Lakes, connecting waters or the Saint Lawrence River (where that river forms part of the Canada–United States border)

>Any lands reserved or acquired for the use of the United States, and under the exclusive or concurrent jurisdiction thereof

>Any island claimed under the Guano Islands Act

>Any US aircraft flying over waters in the same manner as US vessels

>Any US spacecraft when in flight

>Any place outside the jurisdiction of any nation with respect to an offense by or against a national of the United States

>Any foreign vessel during a voyage having a scheduled departure from or arrival in the United States with respect to an offense committed by or against a national of the United States

>Offenses committed by or against a national of the United States in diplomatic missions, consulates, military and other missions, together with related residences, outside the US

As you can see, most counties claim jurisdiction over offenses against their citizens, including the US. This is hardly rare. The moment he entered US soil, he was fair game for arrest as generally arrests on US soil are legal (with reason of course - probable cause and all).

For example, if a US citizen was murdered, usually the host country would try to prosecute. Murder is generally looked down upon. If they did not, you bet the US would try to prosecute.

When Somali pirates took US citizens hostage, you bet the US was going to get involved and not ask the Somali government politely to help. They wanted to make sure the rescue got done. Would you suggest they ignore it in that case too?