The fourth amendment does not outlaw all searches without a warrant; it outlaws all unreasonable searches and seizures.
The reasonableness standard generally requires that searches conducted in the course of ordinary criminal law enforcement require a warrant. However, the Supreme Court has long recognized that special circumstances, outside of criminal law enforcement, can justify a departure from the warrant requirement. Foreign intelligence collection, especially in the midst of an armed conflict in which the adversary has already launched catastrophic attacks within the United States, fits squarely within the special circumstances exception to the warrant requirement.
Your statement at #564 came across as a bit more categorical than that, which is why I had the reaction that I did.