To that point, it's worth noting here friendly fire incidents happen all the time in war, as well as attacks against neutral parties. For instance: the US has bombed its own troops probably more times than anyone can count, and it also bombed the Chinese embassy in Belgrade and shot down an Iranian airliner. Why would they do such things? Honestly, it's plausible they they may actually have had the memory of a goldfish, at least occasionally.
Because an imputed motive is not proof of anything, and there's no way "accounts on the ship" could provide the information you claim they do (knowledge of the attackers mental state).
I don't think anyone disputes that the Israelis attacked the ship intentionally, but you can say the same about most friendly fire incidents. The question is if the people who made the attack deliberately decided to attack what they know to be an American ship.
The sailors would know because they have access to the same information that you do, but a greater incentive to actually do the reading. The Israeli pilots knew it as a US ship, their radio traffic questioning their attack orders - after visually identifying the USS Liberty as a US ship, was recorded and the transcripts widely known about. This happened several times, so unless the Israeli command center had the memory of a goldfish - they intentionally kept sending attack aircraft until they eventually got a pilot to pull the trigger. Why would they do such a thing? Because the US wasn't onboard with the Israeli preemptive strike and they didn't want a signals intelligence boat tipping off the Egyptians. Israel doesn't appear to reciprocate the fond feelings expressed by American politicians - the mere idea of the "Samson Option" is proof enough of that.