Playing devil's advocate:
Some news sources are not so sure that Apple hasn't given China some extra peeks at their code:
"
In January 2015, the state-run newspaper People’s Daily claimed, in a tweet, that Apple had agreed to security checks by the Chinese government. This followed a piece in the Beijing News (link in Chinese) that claimed Apple acceded to audits after a meeting between Cook and China’s top internet official, Lu Wei. China’s State Internet Information Office would reportedly be allowed to perform “security checks” on all Apple products sold on the mainland. " -
Quartz magazine,
Apple is openly defying US security orders, but in China it takes a very different approach
It's a worthwhile devil's advocate to play, and this is no doubt what the FBI has been using as a PR tool in their "you did it for China" claims, but this would mean that Cook has lied in very explicit terms when he refuted these claims in the media.
It's also possible that the "security checks" mentioned involve as-shipped products, which would be no different from products provided to, say, the FTC for testing. If Apple gives the Chinese government an as-shipped product to do security testing on, that's not any kind of violation of trust or security--they're just allowing the Chinese government to do whatever tests they want on a product they make, similar to what any organization might do in the way of safety or compliance testing.
China might well do this in order to make sure that their security agencies still have a secret hack that works (like the NSA might as well), but that just means that Apple has flawed security, not that China got special access.
A security audit (based on my own experience with such things) could be the same thing; it could be looking at the practices you have internally to confirm, for example, that you're not leaving yourself open to hacks or intentional intrusion by a different government. Depending on the scope of the audit, that again wouldn't necessarily violate any kind of trust or security--it doesn't let them modify the software customers are getting.
The organization I work for has undergone exactly such things with non-government auditors for certification in the past, and they were structured such that security could be confirmed without disclosing any private data. Now, depending on level of access, the Chinese government could hypothetically try to use what they had learned from the audit to generate their own hack, but again that would just mean that Apple has a weak system, not that they were intentionally letting a government cheat around it.
If Apple is giving the Chinese government actual code, or a known route to bypass user security features, or information that they know to expose weaknesses in their system, to China, then that would be a different situation entirely.
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So take a chill pill, bro. The whole Edward Snowden incident turned the tech community into a bunch of paranoid delusional nut jobs.
If you are indeed correct about requiring them to go through a US court, then that would reduce--although far from eliminate--the possibility of abuse.
However, the Snowden incident didn't turn anybody into a "paranoid nut job", it just confirmed exactly what many people long suspected was the case--that US security agencies have little respect for legal boundaries, that they have few qualms about data trawling on a staggering scale, and that they're quite willing to spy on friendly governments.
As far as this case goes--which has nothing to do with the Snowden thing, as that was the NSA, not the FBI, and even the NSA (and CIA) are basically on Apple's side in this--I'm not paranoid, I just understand how security and government back doors work in the real world.