If the government laid a subpoena to get iMessages, we can’t provide it. It’s encrypted and we don’t have a key.
It's encrypted and they don't have the key, but since the user does not have any control over the public keys being added, they could add a trusted public key and get it anyway. So they can actually provide messages if they really wanted to.
I don't believe they really want to. But the thing we should've learnt from last year's revelations is (1) that companies can be forced to do so anyway via secret courts; and (2) the NSA is willing to make a 'technical solution' otherwise.
So, Tim Cook is not being completely honest here. Apart from what hardware can do, the only way to trust such an application is if you had the source code, the source code of the operating system and the source code to firmware blobs, and some way to prove that everything was compiled from public source code without modifications. Since that is not going to happen, iMessage should be considered as secure as unencrypted e-mail when it comes to governments. Of course, it does provide more protection than e-mail against less equipped actors.