It depends upon the implementation of the "backdoor": If the government had a heavily guarded server that held the only copy of a private key that was the pair

It depends upon the implementation of the "backdoor": If the government had a heavily guarded server that held the only copy of a private key that was the pair of a public key that all asymmetric encryption added as a mandatory target (just like a PGP recovery key in the enterprise), and law enforcement could pass messages through it, with a coupled court order and with civilian oversight, and public text popped out, it could be secure. But that isn't how they would do it.