Please see the most recent updates in the "Where did the .com name go?" thread. Posts number 16 and 17.
Makes sense to me. I'm given to understand it essentially means no US military force of any size can cross another nation's border and enter that nation for any mission without the expressed verbal and (later) written authority of the POTUS. US military units that are already within that nation's borders, on the other hand, can be ordered by their area commanders (SACEUR, COMAFRICOM, CIA Chief of Station, etc) to carry out operations within the borders of the country they are already inside of, with the knowledge of the host nation, to protect American interests within that nation. Like you said, this keeps some area commander, or individual unit commander, or red hot throttle jockey in hot pursuit of another aircraft, or a mixed-up SEAL team, from entering another country on their own or at their commander's behest - that authority has got to come from the President, and no one else. I'm told this authority can not be delegated.