It is unlawful for any person who is subject to the jurisdiction or control of the United States, directly or through any subsidiary or affiliate to operate a private remote sensing space system without possession of a valid license issued under the Act and the regulations.
"The Act" there refers to the National and Commercial Space Programs Act (NCSPA or Act), 51 U.S.C. § 60101, et seq, which you can find here.
NOAA page on how to get a license under that act, etc, is here. A recent Wired article covers it pretty well.
NOAA's governing regulations limit the scope of its regulation: "For purposes of the regulations in this part, a licensed system consists of a finite number of satellites and associated facilities". That "satellites" term separately has a general definition that rules out anything not in a "permanent" orbit, alternately a "stable orbit", i.e. a launch vehicle. What might be new is that the Falcon 2nd stage does achieve a "stable orbit" for Iridium insertion, hence the signal cutoff.
And now NOAA has issued a statement that says they did put a restriction in place, but doesn't say why.