Kidd absolutely attacked ships on the high seas, killing sailors in order to steal their cargo, so from a moral standpoint you can interpret that as you see fit. It's the legality of the situation that made Kidd's case interesting and tragic.

Captain Kidd's defense when he was caught and brought up on charges of piracy was that he was actually a special class of pirate known as a privateer. Privateers were sailors commissioned by governments to attack the merchant vessels of enemy nations. So, for instance, if you were English and England was at war with France, as was the case for Kidd, you might be able to get special permission to attack French ships as a form of economic warfare.

Privateers carried on them, at all times, official documents - called "letters of marque" - entitling them to attack these foreign vessels. If you were caught pirating by officials from your own country, you just show them your letter of marque and they let you go (of course, if you were caught by officials from another country, they'd treat you the same way they'd treat any other pirate).

So when Kidd got on the witness stand and said he was a privateer, it should have been easy to prove, but for some reason he didn't have his letter of marque with him. To complicate matters, the copy kept in the official records back in England was also lost. So, unable to prove that he was actually a privateer, kid was executed and his body hung in chains on public display for three years as a warning to other pirates.

So what happened to the paperwork that should have cleared him? We're not sure how it happened, but Kidd's letters of marque were found misfiled with a few other odds and ends in the early 20th century, about 200 years too late to stop the execution. I also saw an article a few years back that claimed that Kidd's personal copies of the letters had been found sewn into the lining of the jacket he had been wearing when he was captured (although I have not been able to find the article again since then, so grain of salt here). The question then is whether the papers were misfiled and Kidd denied access to his jacket due to a series of official blunders, or whether there was some kind of conspiracy against him. The conspiracy theory is actually the most likely, as Kidd was originally backed by some of the most powerful men in the English court at the time, and it seems unlikely that they would have just forgotten about him. Tales of murder and torture had made their way back to England while Kidd was out voyaging and it is likely that those who originally supported him believed these rumors (which there is evidence to believe were overblown or inaccurate) and didn't want their names to be associated with him any longer.

So completely morally innocent? Probably not. But he was more or less legally innocent and was probably executed illegally.

His lasting fame came largely from his botched execution (the noose broke the first time, which was colloquially viewed as a sign from God of the innocence of the accused), and he was rumored to have buried treasure on an island somewhere, giving rise to the legend of pirates burying treasure. He did in fact bury a small amount of money, but it was excavated by the local governor and shipped to England as evidence in Kidd's trial. No further historical record exists, to my knowledge, of pirates burying treasure, or any person finding treasure buried by pirates.