If we didn't have a free press nobody would even know about Snowden.
If the press didn't report on Snowden and Manning, people would know about them. But the message wouldn't be controlled.
Remember when the news of Manning's leaks first broke? When Wikileaks published that video of the U.S. military gunned down a bunch of journalists in Iraq from a helicopter (irony level #1)? That got everyone's attention, and then Wikileaks made public announcements to the effect of "Ok, we have a huge trove of government records that was handed to us by this anonymous source. We want to handle this information responsibly, and there's no way we can process all of this in a responsible fashion by ourselves. So we're going to share it with a bunch of other reputable news organizations, and we'll all be releasing information as we're able to read it all, redact, and make sure we understand what we're publishing to ensure no unintended consequences." And all the major media outlets corroborated this. Then government officials started talking about wanting to assassinate Assange (irony level #2). So in order to protect himself, he put a highly encrypted file out to the public containing the leak, promising the keys to it would be released if anything happened to him. The major media outlets got all kinds of juicy content out of the deal, but as the government got more and more shrill about it and Manning became a public name, their narrative about the nature of the leak shifted to "THIS MANNING GUY JUST RECKLESSLY DUMPED A WHOLE BUNCH OF INFORMATION ON THE INTERNET - HE SHOULD BE LyNCHED, RIGHT?".
You can call that free press if you want, but I challenge anyone to say that there's not some serious fucking issues there.
And as a more general comment, I don't give a shit about what's technically legal if it doesn't work in practice, and I don't take examples of people having to put their lives on the line just to create specific examples of rights being enforced as a reliable indicator that those laws are properly functioning. To me, it's a sign that many more people have probably backed down instead, and whatever's guaranteed by law didn't do shit for them.
Also, can we talk about how law enforcement consistently gets away with specifically targeting journalists to prevent documentation of their illegal abuses at protest events and the like? If we have a free press, there should be legal consequences to that behavior.