I note that you're not mentioning the actual fact checking sites that you believe to be subverted, nor specific stories that serve as examples of this subversion.
I've seen criticism of Snopes, for example - but apart from one or two examples of cock-ups that they corrected, I've never seen any evidence of subversion - so which sites are you talking about?
Snopes is one of them, surely, that I've seen lots of partisan propaganda, especially on political topics (of course, it's hard to put propaganda into a topic like "did a woman in Florida marry an alligator and gave birth to alligator-headed twins?" so it's in political topics). But I purposedly didn't name specific one because they are all like that - snopes, politifact, fatcheck, you name it. I'm not talking about specific screwup of specific outlet, you can always explain it away, I'm talking about how things are developing (at least how it looks to me) in general.
"Partisan propaganda" isnt the largest issue, even if you find support of it. Fact-checkers just cant scale to the meet the production of news per day. Not possible. Not even with 10 trusted Snopes-like organizations. Snopes produced 830 stories in 2016 under their "News" topic. Thats 2 stories a day. CNN produced over 35,000 stories last year... then there is NYT, HuffPo, WaPo, Fox, MSNBC, Hill.........
I would but that would not achieve any useful purpose - any specific example I give can be either claimed as genuine disagreement and lead to a prolonged discussion that would derail from the topic completely, while arriving at no useful conclusion, or dismissed as either "it's small change, that's all you got?" or "this is just one example of no true Scotsman, true Scotsmen are different".
But ok, here's an experiment. Not snopes (I have snopes examples too, just requires a bit more time to find).
Bernie says black youth real unemployment is 51% - Politifact says it's mostly true[1], maybe even over that. Maybe the terminology was a bit off, but the point of high black youth unemployment is correct. Not completely true, but mostly is.
Trump says black youth unemployment is 59% - so Politifact says it's close to true, but probably closer to 51%, right? Trump is close to truth, but maybe exaggerated a little, as is his habit? Nope, Politifact says it's mostly false[2] and the real figure is a third of that. Note how in the first case PF is completely OK with extending unemployment definition but turns rigorously pedantic in the second case and insists unemployment is nothing but the figure published by BLS, and Trump's point - which is exactly the same point as Sanders had! - is total bullshit. How do you like them apples?
Ron Paul says there was no income taxes until 1913? Half true[3], there were short-lived efforts to introduce the tax (as if that was the point). Jim Webb says the same? Fact check is now "mostly true"[4]. This one was corrected postfactum, because somebody noticed and made fuss out of it.
There are many more examples of PF doing this - spinning the facts depending on who said it. Snopes is doing the same, and more - like taking a factually true statement, finding some retelling that adds a slight exaggeration or twist to it and slapping "mostly false" on it and dedicating most of the article to refuting that slight twist and ignoring the original fact. Because while the initial fact is true, this particular exaggeration or twist is not, so the compound statement is "false" and now the original statement can be reported as "found to be mostly false by factcheckers". Primitive manipulation, but it works.
A simple google search will provide you with numerous examples, even of Snopes in particular. Here's one[0] by Snopes where the True/False statements don't even match the claim. It's obvious the "fact checker" (i.e. journalist) contorted the argument to reach a desired conclusion.
So I've just had a look at that. The True/False statements seem to match the claim pretty closely - which elements in particular make you think otherwise?
I've seen criticism of Snopes, for example - but apart from one or two examples of cock-ups that they corrected, I've never seen any evidence of subversion - so which sites are you talking about?