Ah, hence the confusion. Here's the NOTAM:
ALL FLIGHT OPERATIONS IN THE OVERWATER AREA OF THE TEHRAN FLIGHT INFORMATION REGION (FIR) (OIIX) ABOVE THE PERSIAN GULF AND GULF OF OMAN ONLY ARE PROHIBITED UNTIL FURTHER NOTICE DUE TO HEIGHTENED MILITARY ACTIVITIES AND INCREASED POLITICAL TENSIONS IN THE REGION, WHICH PRESENT AN INADVERTENT RISK TO U.S. CIVIL AVIATION OPERATIONS AND POTENTIAL FOR MISCALCULATION OR MIS-IDENTIFICATION.
I guess the logic is that any potentially trigger-happy units are likely to be afloat or on the coast. Hopefully there aren't any.