This has already been done. During Operation Aurora the Chinese hacked into the FBI backdoor built into GMail by Google and used it to gather information about intelligence operations being performed by the United States against Chinese nationals and also used it to perform surveillance of their own against their terrorist and dissident watch lists.
There are probably more examples.
I do not know of a single database that has 'all the keys' to the all software and encryption back doors. If such a thing existed it would be a very valuable target. Somehow, though, I imagine that there isn't such a centralized database.
[citation needed]
https://www.google.com/webhp?sourceid=chrome-instant&ion=1&e...
I'm not sure we want to base policy on something speculative like that. Agreed that conversations should be had - both about widespead backdoors and about centralizing the keys to these backdoors - if the scenario ever comes to pass.
In the meantime we can't say that the backdooring contributed to this Chinese attributed breach.
The way the US government would be likely to handle this situation is that they would recognize the threat and mandate that no such single database be created or that one be separated were it to exist. I don't know that they would change their mind about backdooring products and services when they can mitigate the scenario and address concerns a much easier way.