The key you're forgetting about freedom of the press is that it cuts both ways.
The contract the press has with the public is "Sure, you're allowed to print whatever you wish, but don't expect us to BELIEVE you once you've exhausted all your credibility (and we don't believe you by default)". Likewise, if you continuously deliver relevant information and editorial you will be rewarded with higher readership/viewership and trust. No, this isn't perfect, but it beats the bejeesus out of a state controlled news service (which, btw, we DO have , it's called CSPAN and NPR but the masses here in the U.S. can't be bothered). What I'm saying is essentially to let the free market do it's job. It won't always be perfect, but at least if you hate it you can try to change it without cutting through loads of bureaucratic tape.
Now on to this law. What? Yes you want a law. You want to force the "press" to abide by a subjective regulation of reporting on the "truth". Leaving aside the obvious axioms of math and physics, "truth" is different to many people. My truths may not be your truths, so I'd like "truth" presented in a way that reflects my bias. And that is all the press is doing.