No, that's not it.
A free press is "free" because it's unconstrained by a Government or capricious regulation, not because it "goes against the government's views". Sometimes members of a free press will support the government, other times they won't.
It's not a priori virtuous to go against the Government's views. Sometimes the Government is right and sometimes it's not. Like everyone else.
You're right it's not inherently virtuous to go against the Government's views. But it is inherently bad to push government views in exchange for preferential treatment which is what appears to be happening here and with the National Enquirer.
If you are concerned about a free press, you should be equally concerned about the commingling of government and press such that the government captures certain media properties and converts them to state run media. Free press means a separation of government and press; any governmental involvement damages a free press.
Add to that monopolistic corporate power.