The New York Times columnist — and former Fortune editor — waited until the end of Saturday’s 1,700-word “Talking Business” column about the health of Apple’s CEO and the secrecy that surrounds it to reveal that on Thursday afternoon, several hours after he’d gotten his final “Steve’s health is a private matter” from Apple’s public relations machine, he got a call from Steve Jobs himself.

“This is Steve Jobs,” he began. “You think I’m an arrogant [expletive] who thinks he’s above the law, and I think you’re a slime bucket who gets most of his facts wrong.”

Jobs, according to Nocera, said he would share some details about the health condition that made him to look so thin and haggard at his last public appearace — and triggered two share-punishing rounds of speculation on Wall Street — if Nocera agreed to keep the conversation off the record.

Nocera agreed, and reported only that nothing Jobs told him …

“contradicted the reporting that [Times reporter] John Markoff and I did this week. While his health problems amounted to a good deal more than ‘a common bug,’ they weren’t life-threatening and he doesn’t have a recurrence of cancer.”

The “common bug” is a reference to the explanation for Jobs’ weight loss that Apple’s PR department put out in June — an explanation that Nocera feels fell somewhat short of the truth. Markoff reported on Wednesday that Jobs had had an unnamed surgical procedure earlier this year related to his loss of weight, and Nocera adds that he had learned that Jobs was having ongoing digestive difficulties stemming from the cancer surgery he had four years ago — the details of which were first reported by Fortune (see here).

All this leads Nocera to the broader point he wants to make about Apple:

“Apple simply can’t be trusted to tell truth about its chief executive. Under Mr. Jobs, Apple has created a culture of secrecy that has served it well in many ways — the speculation over which products Apple will unveil at the annual MacWorld conference has been one of the company’s best marketing tools. But that same culture poisons its corporate governance. Apple tells analysts far less about its operations than most companies do. It turns low-level decisions into state secrets. Directors are often left out of the loop. And it dissembles with impunity.” (link)

So, yes, Nocera thinks Steve Jobs is an arrogant [expletive] who thinks he’s above the law.

But Jobs may have the last laugh. Twice in his column, Nocera refers to things that happened during Apple’s (AAPL) third quarter conference call on Tuesday afternoon.

In fact, the conference call happened on Monday.

UPDATE: The error in the printed edition of the paper has been corrected in the online version.