They really didn't.

Going off my other comment...

• Homeland - Callsign of Air Controllers
• Samuel Kislev - Chief Air Controller at Kirya, this is the controller who actually orders the initial attack on the Liberty.
• Gloria - Deputy Chief Air Controller at Kirya
• Menorah - Flight of Four Mirage IICJs armed with several 500 lbs bombs. They are a kind of priority flight for all the air-controllers since they are delivering a strike package of some sort elsewhere against Egypt.
• Menachem: Chief Air Controller at Air Control South (near the Sinai border)
• Yigal: Deputy Chief Air Controller at Air Control South
• Robert: Chief Air Controller at Air Control Central (25 miles south of Tel Aviv)
• Shimon: Deputy Chief Air Controller at Air Control Central
• Kursa: Callsign for the two Israeli fighters who made the initial attack
• Royal: Callsign of two Israeli fighters who made the 2nd attack
• Migdal: Only Israeli Torpedo boat with a working radio
• Chalon: A single Mirage IICJ

The transcript from the flight controllers, starting at 1343, Saini Time

Unknown: Navy recieved a report that two miles at sea, off El Arish, thre is something that's pounding El Arish. Their torpedo boats are going towards there.

Gloria: I heard. I took helicopters from El Arish. I spoke withhim. He went out to have a look and says he doesn't see a thing.

Unknown: There's contact witht he field but not within the city.

Kislev: Yigal, have Chalon take a look.

Yigal: Chalon.

Kislev: Clear.

Shimon: Robert, have him take a look. He's circling the same area.

Kislev: Can you see him, Shimon?

Shimon: Yeah. Sure, Yigal, can you see route 4? Have you informed him of 20,000 feet altitude?

Unknown: Do you have Tiyeh 39 10? [Tiyeh is the phonetic pronunciation of the 9th letter of the hebrew alphabet. This is a grid location.]

Unknown: Tiyeh 39 10, one moment.

Kursa: We're switching to military power. Affirmative, northern direction. Fuel okay, 3000 [the Kursa flight has just been directed towards what would end up being the Liberty].

Yigal: Robert, where is Menorah now?

Kislev: Forget about Menorah. Yigal, you have a ship at 26 [this is a site designation]. Take Kursa over there. If it's a warship, then blast it.

That last command was given at 1350. It took a grand total of 7 minutes for the first flight to be instructed to fire upon the ship that is actually the Liberty. The Air Controllers don't know it's American, and the Israeli Navy has mistaken her for a destroyer that's shelling a ground position. The pilots who were ordered to attack her, don't even have her on their radar yet.

Just to be clear on how silly this kind of is, Kursa would be asked by the patrol boats who'd launched the attack to identify the ship.