This implies it is possible for Apple themselves to apply an iOS update to a locked phone in order to disable the erase-on-repeated-failure feature.
Tim Cook doesn't offer an opinion about how possible that might be. As a matter of principle, he doesn't believe that Apple should be forced to make the attempt.
That doesn't stop anyone else from doing so, however. And I suppose that the FBI could seek discovery on all requisite information, take depositions, etc, etc. However, I vaguely recall that discovery can't compel production of new work product. But maybe that's just a limitation in civil litigation.
It seems like their stand would be better saved for when a compromise is requested that is actually possible for them implement.
Because the larger principle is what's really at play here. Whether Apple can do what the FBI asks, or not, is irrelevant. What is relevant is that what the FBI asks is bad. Even if Apple can unlock this phone because of shortcomings of the 5C (versus later model), it sets a bad precedent for later, especially if Apple truly cannot unlock the 6s and beyond ("you could do it on the 5, why not an iPhone 7?").
I'm no lawyer, but I'm of the opinion that this is a legal crowbar for later cases, and the Feds are using a tragic incident to drum up support ("you don't support terrorists, do you?")
As Tim Cook says, it would be a bad precedent. And obviously bad PR for Apple to admit vulnerability.
It won't get unlocked by that, because as soon as the new iOS takes over, it will detect the activation lock and require the Apple ID password to be provided. Also, going through iTunes erases all the data.
But presumably a custom DFU update can only replace the OS without replacing the data. The iPhone doesn't try to protect against valid updates, and will happily run anything signed by Apple; the locked/unlocked state is only about the encrypted user data on the device.
A large percentage (and presumably the the target in question) will willingly (at least today) upgrade their iOS to whatever Apple pushes out - we don't (for the most part) even question whether the purpose of that security patch is to reduce security.
The only thing that secures an iPhone is the iOS following the rules of security such as the security enclave - it can just as easily (in a new release of iOS) be instructed to ignore it.
What Apple/Tim Cook are doing here, is standing up for the importance of not being required to hodge-podge be at the whims and mercies of police agencies that demand they do whatever is required of it.