Tim Cook’s apology did its job. Apple earns respect in China.

Cook visiting a Chinese factory last year. Photo: Apple/AP

FORTUNE — Tim Cook’s public apology to Apple’s (AAPL) Chinese customers was being quoted at length Tuesday in the very print and broadcast media that for a fortnight had been ripping the company apart for its greed, dishonesty and “unparalleled arrogance.”

“The company’s apology letter has eased the situation, softening the tense relationship between Apple and the Chinese market,” wrote the Global Times. “Its reaction is worth respect compared with other American companies.”

The Foreign Ministry praised Apple for “conscientiously” responding to consumers’ demands, according to Reuters.  “We approve of what Apple said,” spokesman Hong Lei told reporters at his daily news briefing.

There were plenty of critics Monday who said Cook’s letter and the changes he made in Apple’s repair policies in China were a big mistake. Steve Jobs, they said, would never have apologized for customer service that, as most of Apple’s customers in China know, is second to none.

But Jobs never set foot in China. Cook, on the other hand, built Apple’s Asian supply chain, and he knows something about navigating the complexities of official relations in the Far East.

It won’t cost the company very much to repair broken iPhones with new parts or extend their warranties — basically giving China’s state-run media everything they asked for.

It cost Cook nothing “sincerely apologize” and to say, as he did in his letter:

“We recognize that we have much to learn about operating and communicating in China, but we want to assure everyone that we bring the same deep commitment and passion to China as we do to any other part of the world. This commitment, a desire to delight all of our customers and provide them with an extremely high-quality experience, is deeply rooted in the culture of our company. And we will not rest until we achieve this goal.”

That kind of language can save a lot of face, on both sides of the Pacific.

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