The USS Liberty was not sent to help the Israelis. It was sent into the area, in international waters, to listen in on radio communications by the Egyptians. There was some evidence that Russian pilots were operating Egyptian aircraft as well as manning missile batteries.
If you really want to learn what went on, I suggest you go deeper into the link beyond reading just a few statements. The evidence is overwhelming that this was a deliberate attack.
I will research it as you suggest. I hope I can come up with a better explanation than you though as far as motive. My gut is that it was an accident or possible something more sinister but by an small faction. I need a motive and there are too many issues with the conspiracy theory. If Israel wanted to sink the ship and leave no survivors they would have done just that. Furthermore they didn't need us 'in' the war, they handled it fairly well themselves if memory serves. Additionally the ship was sent to help them by monitoring the enemy and those are the words from your own link. An interesting subject and a sad day no matter how you slice it. I'm not a consipiracy buff however and believe the truth in most 'conspiracies' is often boring and a result of ignorance or errors.