No, they frequently run leaks which they think are in the public interest. And they have pretty low standards for what they think is in the public interest -- ultimately they just need to be able to come up with a good justification for believing it might be in the public interest, since their primary purpose is to sell newspapers.

They would refuse to leak random diplomatic cables which don't show any wrongdoing by anybody, though. (Although they're quite happy to publish a story about them if someone else is responsible for the leaking.)