Cook could have lied and said building a special OS was impossible. But he didn't because he knows someone will find out. When you're facing a subpoena, you don't knowingly lie.
Not that I believe Apple's CEO is lying, however…
You don't knowingly lie if you think the risk of getting caught is unacceptably high. That last part is important, I think, and indeed, you state, "because he knows someone will find out", so I know you get it. However, I don't think we should forget that a great deal of the concern we have presently in this thread about the government's capability in introspecting our technology is indirectly the result of the DNI lying under oath¹.
¹I know your post says subpoena, but it seems similar enough that its worth reminding…
Additionally, that letter is written with very carefully fuzzy language so as to remain true-ish.
As in, Apple can't make this change and guarantee that nobody else will use it. In the same way that any software change (which they do regularly) could open up a security flaw. That doesn't mean it's likely, or any more likely than any other software update.
I wouldn't put it past the NSA to have snapped up a former iOS developer for explicitly the purpose of breaking into iPhones. An ex employee could certainly call him out.
> Additionally, that letter is written with very carefully fuzzy language so as to remain true-ish.
Cook is trying to be as clear as possible to a public who doesn't understand encryption or why Apple is standing up to the FBI. That's a lot to swallow, and yes his letter is carefully worded for good reason. Given that there is a backdoor that Apple could create, it's not unthinkable that with more details, 3rd parties could figure out how to get in too.
This sounds like a misunderstanding. No clever third parties are going to find a way to break code signing. To exploit the security hole Apple already created would require having Apple's signing certificate so that a phone could install the code. If it wasn't for the certificate, it would be quite a bit more trivial to hack a firmware to do a malicious thing and install it on any phone.