I'll go further. We need at least two webs of trust.
Would you trust a Democrat to fact-check Trump's claims of election fraud? Would you trust a Republican? In fact, you should trust the Democrat if they say the claims are true, and the Republican if they say the claims are false.
Ideally, we'd get one set of fact-checkers that both sides trust. In practice, that may not be possible. But at least, if we have separate fact-checkers for each side, if they agree, then we have a fairly good basis for suspecting that they're right.
Would you trust a Democrat to fact-check Trump's claims of election fraud? Would you trust a Republican? In fact, you should trust the Democrat if they say the claims are true, and the Republican if they say the claims are false.
Ideally, we'd get one set of fact-checkers that both sides trust. In practice, that may not be possible. But at least, if we have separate fact-checkers for each side, if they agree, then we have a fairly good basis for suspecting that they're right.