I don't think it's a computer science claim to begin with. To my knowledge nobody has ever broken 256-bit AES, but that's not the part of the system that fails. There are two things that prevent it from working in practice:

The first is that "us" would be something like "governments in the US"; but then that's too big of an organization to sustain as free from compromise. There are tens of thousands of judges in the US, well over a million police and military. All it takes is one of them to be corrupt or incompetent or lazy and the bad guys get to use the skeleton keys to everything in the world, which can unlock secrets worth billions or get people killed. And that's assuming they only compromise the authorization system; if they actually gets the keys it's practically armageddon.

And the second is that it's not just one government. If the UK makes Apple and Google build a system to unlock anybody's secrets, is Australia not going to want access? Is China? Let's suppose we're not going to give access to Russia; can the fallible humans operating this system fend off every attack once the FSB has been ordered to secure access by any mean necessary?

It's a system that combines many points of compromise with an overwhelming incentive for everyone from state-level attackers to organized crime to break in and severe consequences when they do.