That is the best case scenario. The worst case scenario is when one of those is prohibited from publishing "fact checks" because they "don't meet our high standards" (which Google is free to set as they see fit) and the other is free to declare "false" anything opposing tribe says because everybody knows they're the bunch of damn liars anyway.
Also, "fact checkers" are free to misinterpret the content of the article, i.e.:
"Increasing the minimum wage helps improve the economy"
* Fact check by Conservative-example:
Claim: "we should take all the money away from successful people and give it free to drug addicts and moochers"
Verdict: false
* Fact check by Progressive-example:
Claim: "we should let poor people to just die from hunger"
Verdict: false
etc. Neither of that contributes to the discussion much, in fact, it makes it harder by caricaturising positions of opposing sides and making it harder to discuss arguments on the manner, while wearing the veil of "objective fact checking". The expression "fact checking", which once meant verifying objective facts, has already been hijacked by propagandists to make their propaganda more plausibly sounding. I predict more such abuse is going to happen and the term would be further eroded until it's completely meaningless.