I smell word games. "Constitutional" can mean not prohibited by the Constitution, or it can mean actually granted by the Constitution. If it's merely not prohibited by the Constitution, then there's nothing saying Congress can't regulate it (or prohibit it).
It flows naturally because of the long-established proposition that the Constitution trumps the law
Only when they conflict. You wouldn't be assuming the very point in dispute, would you?
The cases I cited made it abundantly clear that the courts were speaking of the President's "inherent constitutional authority", in others words, a power granted by the Constitution, and therefore s power that may not be infringed upon by Congress.
I'm only assuming that the court meant what it said when it held that the President did have inherent constitutional authority to conduct warrantless searches to obtain foreign intelligence information. And since, as the court held, this was a constitutional power of the President, it can't be infringed upon by Congress.