Correct, which means that even if the surveillance fails to intercept communications of any US Persons, it can still violate the law, if it was conducted recklessly without regard to status.
So you have a Catch-22: Either the administration failed to confirm immigration status and violated the law, or they did take the time to confirm immigration status, in which case why on earth didn't they get a FISA warrant (which would have been faster anyway)??? I'm thoroughly confused.
Although you quoted...
"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
...you seem to have skipped over the word "UNREASONABLE" a little too quickly.
IMHO, it is perfectly REASONABLE for our President, in war-time, to search the international air-waves for conversations between enemies who are plotting to kill Americans -- even if some of those enemies happen to be standing on U.S. soil.
Do not take this personally, but what kind of idiot would a person have to be to conclude that "the law" permits us to dispatch a cruise missle to kill Osama bin Laden, but does not permit us to listen to his phone calls to "sleeper cells" located in America?