No, that's incorrect, the court never said, nor implied any such thing. The court's conclusion was explicitly based solely on the President’s constitutional responsibility to conduct the foreign affairs of the United States.
But this claim of yours is a perfect example of the mental, logical and legal contortions you've been going through in a hopeless attempt to find some way to invent limits on the President's constitutional powers, powers which all the courts cited above have concluded belong inherently to the President.
First you invented out of whole cloth your own novel standard of evidence that an agent of a foreign power had to be "known" to be such before surveillance could be commenced. Never mind that neither the court nor the law ever articulated such a standard. And then to support your contention, you vainly attempted to place such words in the mouth of the court and the words of the law, when none existed.
When your illogic was pointed out to you that your "known" requirement far exceeded even the "probable cause" requirement for obtaining a conventional criminal search warrant, you dropped your "known" standard and began substituting the probable cause requirement, insisting that it was the "real" standard by which reasonableness should be determined.
But since virtually all courts to have ruled on the matter have held that the warrant requirement is inapplicable to the President's inherent authority, then so to is the probable cause requirement. What is left is simply a determination of whether the government's surveillance was "reasonable".
But what makes all your considerations moot and irrelevant, is that by the time any court becomes aware of such surveillance, it will only be because the case has ripened into a full-fledge intelligence or criminal case, that would not be before the court had there NOT been a reasonable cause to proceed in the first place.