They're in favor of a free press, except if that press isn't in support of their political agenda. Then all of a sudden that free press isn't supposed to be so free.
If the freedom you want has a required political position, it's not freedom that you want.
Just like how they only use “free speech” to defend the indefensible things they say. Because they can’t actually justify the things they say, so they fall back to “well you technically can’t stop me from saying it.” The “free speech” defense is just about the lowest bar you could find, and if you’re using it you should seriously examine why you’re saying the things you are. Because if you’ve fallen into the “free speech” defense, it means you have no other defense.
It's definitely not that. They are just pointing out that the right to free speech prevents the government from impeding someone's ability to say something, it doesn't (despite implications made by a lot of people who cry out that their right to free speech is being impeded) force others to listen to or agree with that thing being said. If anything, the people that abuse the name of free speech by implying that it means people need to agree with them, or need to amplify their message, are attacking free speech by mudding the water around what it means and making it harder for good faith entities to invoke that right