According to this official US Navy document the US Navy was indeed conducting live fire testing of missiles off the coast of California durning the Mystery Missile Launch ovar L.A..

From page 55.
"434/10(18).
EASTERN NORTH PACIFIC.
CALIFORNIA.
MISSILES.
1. INTERMITTENT MISSILE FIRING OPERATIONS 0001Z TO 2359Z
DAILY MONDAY THRU SUNDAY IN THE NAVAL AIR WARFARE CENTER
SEA RANGE. THE MAJORITY OF MISSILE FIRINGS TAKE PLACE
1400Z TO 2359Z AND 0001Z TO 0200Z DAILY MONDAY THRU FRIDAY
IN AREA BOUND BY
...
3. VESSELS INBOUND AND OUTBOUND FOR SOUTHERN CALIFORNIA PORTS
WILL CREATE THE LEAST INTERFERENCE TO FIRING OPERATIONS
DURING THE SPECIFIC PERIODS, AS WELL AS ENHANCE THE VESSEL'S SAFETY WHEN PASSING THROUGH THE VICINITY OF THE SEA RANGE
IF THEY WILL TRANSIT VIA THE SANTA BARBARA CHANNEL AND WITHIN
NINE MILES OFFSHORE VICINITY OF POINT MUGU OR CROSS THE AREA
SOUTHWEST OF SAN NICOLAS ISLAND BETWEEN SUNSET AND SUNRISE.