News Obama sides with Cameron on cryptography stance

That's basically how all public key cryptography works, but you're misremembering a little bit: asymmetric (public-key) is slow, symmetric (shared secret) is fast. Asymmetric works by generating a unique symmetric key, which is then encrypted using the asymmetric algorithm. The result: a block of ciphertext which requires the asymmetric algorithm's private key(s) to decrypt, even though the actual data itself is encrypted with a faster symmetric algorithm using a 'shared' secret (the 'sharing' taking place within the actual encrypted file itself.)

What you could do, and what you may be suggesting - it's early, I might have misread your comment - is add the government's asymmetric public key as a mandatory recipient. That way, the ciphertext will be decryptable by its intended recipients plus the government, but nobody else. Right until some low-level employee who shouldn't have had access in the first place leaves a laptop with the private key on a train, of course...