Why would they nuke Israel if they think of a soviet attack?
The fleet commander followed standing policy to react to any attack on American warships and launched his Ready Five attack assets. It wasn't until the planes cleared the Cats that everyone realized that they were only armed with specials and they were recalled at the order of SecDef McNamara.
Even if the planes had attacked the Israeli ships the weapons would not have detonated because the flight crews did not receive the Nuclear Release codes needed to arm the weapons.
The fact that the aircraft were carrying specials probably saved the Israelis from losing a couple light naval units since the command tree for conventional weapons and the ROE would likely have meant that Washington wouldn't have know about the initial strike until the Israeli torpedo boats, and probably their fighter cover, were sitting on the seabed.
An interesting tidbit about the attack is that Liberty's CO, Capt. William McGonagle, received the Medal of Honor for his actions on 8-9 June, 1967.
Sadly, rather than receiving The Medal from the President in a White House ceremony, as had become a fairly well established practice for living recipients by 1967, Capt. McGonagal recieved his from the SecNav in an unpublicized ceremony at Washington Navy Yard.