Your point doesn't hold together because it seems to be conflating fact checking with bias elimination.
They are obviously different and mostly separate.
A presentation of facts can be biased.
E.g. a news agency can have a characteristic political slant, yet not make up facts to suit that narrative.
When a bias is severe, such that it leads to behaviors like concealing important facts in order to manipulate the correct understanding of a situation, then fact checking can find a problem with it.
We have repeteadly found fake news in the fact checking as well as official truths in the case of Spain and I am pretty sure the pattern is replicated in other places. The funds that bought the newspapers, etc. in Spain are all the same around Europe.
They might not be the same, but they are interrelated sonce this is a fight to monopolize the truth and bias and lies are what you end up seeing. Many times they say sorry and get away with it,, but they are not saying sorry: they are working for some interests.
What happened to Biden's son in Ukraine. They totally disappeared before an election, for example. Why? Why it did not get through and went viral? I do not give a hell from these agencies. They are everything but seeking the truth. Yes, for some irrelevant info they might be ok but we all know who they work for.
Remember part of the leakages that Musk showed when he bought Twitter also with the mail exchanges of what to censor. Only a retarded would believe those agencies at this point.
They are obviously different and mostly separate.
A presentation of facts can be biased.
E.g. a news agency can have a characteristic political slant, yet not make up facts to suit that narrative.
When a bias is severe, such that it leads to behaviors like concealing important facts in order to manipulate the correct understanding of a situation, then fact checking can find a problem with it.