SMA PLT; WITH 3 OTHER ACFT; UNKNOWINGLY FLEW THROUGH TEMPORARY FLT RESTRED AIRSPACE NEAR A PWR PLANT WHILE ENROUTE ON CROSS COUNTRY FLT. THE RPTR WAS NOTIFIED FOR QUESTIONING BY US NATIONAL OFFICIALS THROUGH THE LOCAL POLICE SINCE BOTH THEIR ORIGINATION AND DEST ARPTS WERE UNCONTROLLED.

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AFTER RECEIVING A FLT BRIEFING FROM ZZZ FSS FOR VFR CONDITIONS BOTH TO AND FROM MY DEST; YYY; I DEPARTED FROM WITH THREE OTHER PLANES AS A FLT OF FOUR. MY BRIEFING WAS FOR DIRECT WWW TO YYY AND IN ADDITION TO RECEIVING VERY FAVORABLE VFR FORECAST; THE BRIEFER ALSO STATED; 'NO NOTAMS ALONG ROUTE OF FLT.' I KNEW OF NOTAM RELATING TO PWR STATIONS AND WE DISCUSSED BEFORE LEAVING THAT WE WOULD DIVERT S SLIGHTLY OF XYZ TO GIVE MORE ROOM TO ABC. THEREFORE; THE ROUTE OF FLT WAS WELL S OF ABC AND I BELIEVE COMPLIED SATISFACTORILY WITH THE NOTAM; WHICH STATED TO; 'AVOID THE AIRSPACE ABOVE BCD PROXIMITY TO...' AND 'NOT CIRCLE AS TO LOITER IN THE VICINITY OF...' THE PWR STATION. OUR FLT ENDED NICELY WITHIN MINUTES OF PLAN AT YYY AND WE PROCEEDED TO DINNER. AFTER DINNER WE WERE CONTACTED BY THE LOCAL POLICE WHO WERE NOTIFIED BY US CUSTOMS THAT WE WERE WITHIN 2 NM OF THE PWR STATION. WE DID NOT DEVIATE FROM COURSE OR ALTITUDE (3500 MSL); THEREFORE; WE WERE VERY SURPRISED BY THIS PRONOUNCEMENT. FAA THEN CALLED THE CHIEF WHO INFORMED US TO 'REMAIN WELL CLEAR OF ABC ON THE WAY HOME! TO RETURN; I FLY DIRECT ADB; RECEIVED FLT FOLLOWING FROM XYY APCH THEN PROCEEDED DIRECT REMAINING WELL S OF ABC. ACCORDING TO MY FLT PLAN ROUTE; I WAS A LEAST 5 NM FROM THE STATION AT THE APPROX TIME OF THE INCIDENT. PERHAPS FLT FOLLOWING ON THE WAY TO YYY WOULD HAVE MADE CLEARER OUR INTENTIONS ON THIS TRIP.