What would happen if we made that term (or synonyms like "journalism") protected advertising terms, so that you're required to either live up to it, or call yourself something else?
Another idea under this hypothetical law would be to have retractions/corrections carry the exact same amount of publicization as the original story. In other words, if you spend 10 minutes during primetime talking about something that turned out to be a lie, you get to spend 10 minutes on primetime about how you screwed up. You lie on a front page article that was up for a week? Your correction features in the same place for a week.
This is a labeling/marketing law, nothing more. You are not excempt from those by way of being a media organization. Certainly it is not a speech restriction. As a bonus, it would allow competitors to market on that label since now it actually means something.