For the umpteenth fucking time the "Mainstream Media" is not a loony-right-wing-conspiracy debunking organization. It's a group of outlets owned by billionaires and, less frequently than in the past, giant corporations, who have no interest in truth, just serving a demographic, and most of them repeat the same shit Fox News does, and if they don't they usually are talking about other topics.
You don't know this, because you don't actually follow the MSM, you just assume what's said on various right wing sites or even Fox is true.
At best, the "liberals" have MS Now. That's not because MS Now is a liberal organization - its morning show is literally headed by a man who was considered a far right Republican in the 2000s. It's just that MS Now is pandering to "liberals". Curiously, it's also slightly more honest than the other outlets, largely because most liberals - gweihir being an example of an exception, prefer to know that what they're repeating is true and get embarrassed when called out on it if it isn't.
But no, the MSM isn't sitting watching Fox News saying "Gosh, another lie, we should debunk that". If that were the case, obvious lies, like "gender reassignment is being done on kids!" would be debunked every few days when Republicans make that lie, rather than quoted without pushback.