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What happens when someone yells "Fact check!" at absolutely true things constantly? It erodes confidence. That's why "Person yelling fact check" isn't a typical or generalized role in normal discourse.
Yes, it's good to correct the incorrect. How does one do that typically? A rebuttal.
A supposed 'deferment to experts' on the internet is worth next to nothing, just a way to paint yourself a bit more altruistically while producing FUD.