Apple caved under pressure from China. The explanation Cook gave is not just an embarrassment, it calls into question the veracity of all of his other statements. Why should users believe that (closed source) iMessage encryption is free from backdoors when we know that Cook will dance around sensitive truths? And why should the US government be satisfied with a fully encrypted iMessage given that Apple will cave to d…
That's an easy one: the encryption happens client side and thus any backdoor has to sit on the clients and, if it exists, would be available to security researchers. There is no guarantee of it happening, but I believe some of those researchers reverse engineer whatever binary apple published and then check it for backdoors.
Of course there are still tricks that apple could pull, like adding backdoors only to targeted phones, changing the filesystem to present one version of the binary to the OS command that executes it and another to anyone else (like security researchers), extracting the unencrypted message contents using chips that sit on the memory bus (e.g. baseband), etc. But these tricks are harder to pull off and are still detectable as they happen on end-user devices.
They definitely won't say "yeah there is a backdoor". Ultimately, you need to trust them.