Your example goes too far -- the FBI would absolutely have jurisdiction to investigate the appearance of American children on such a site, as well as to go after Americans who used the site, because that involves the commission of crimes on American soil.

Oh sure they could investigate, I didn't express myself well enough. But they're not going to get much without internal server data. They wouldn't be able to undertake any action against the site, much like American officers can't come to Russia to arrest suspects. They would be wholly dependent on cooperation with local authorities, who wouldn't care at all because it's not illegal in Russia.

> against a child pornography website