FORTUNE — Tim Cook got serious at the 2:20 mark in the attached 4-minute YouTube video.

ABC News’ David Muir had finally stopped peppering Apple’s (AAPL) CEO with questions about the company’s next big thing and brought the subject around to the National Security Agency’s electronic surveillance program.

A top-secret powerpoint slide leaked last June suggested that an NSA program called PRISM gave the agency some kind of backdoor access to Apple’s server farms. Cook did his best to deny it. Again.

“Much of what has been said isn’t true,” Cook told Muir in Friday’s prime-time interview. “There is no back door. The government doesn’t have access to our servers. They would have to cart us out in a box for that, and that will not happen.”

So what information is Apple feeding to the government’s spies? Cook says he can’t tell us.

“We need to say, what data is being given, how many people it affects, how many accounts are affected. We need to be clear. And we have a gag order on us right now, so we can’t say those things.”

See also:

• Apple denies feeding customer secrets to a U.S. spy agency
• What data Apple does and doesn’t share with the cops
• Apple, Jacob Appelbaum and the National Security Agency