That's my feeling too. Integrity is specific to the journalist. It consists of telling the truth as you see it -- and refusing to allow your material to be published if the editor is trying to make you lie in order to please the advertisers, publisher, or anyone else who doesn't agree with you.
Magazines and newspapers have no inherent integrity: only what they can pass on from their journalists. An editor with integrity may decide to kill a story if it would be commercial suicide to run it, but will never change a story just to pander to people.