I think what is trying to be said is that it's in accordance with the US' own laws, not that those laws somehow cause non-US citizens or land to fall under US j

I think what is trying to be said is that it's in accordance with the US' own laws, not that those laws somehow cause non-US citizens or land to fall under US jurisdiction. The only thing that prevents the US from spying on non-US citizens are treaties, and those seem to often be ignored.