Leveling down to the lowest common denominator
As someone posted above, I also care about facts. Many people do.
Sure, quite a few people do not care, and no amount of fact-checking and/or logic and/or pleas for human decency will make a difference to them. Fine. It is always been like that, and always will. That does not mean we should then just give up our will to live, go live in a dumpster, and all that. After all, what's the point, right? No.
There are lots of people out there, all those who are not political junkies, who only started paying attention to this circus after the first presidential debate. They might have "heard" rumors on their Facebook timeline or Twitter or whatever that there was craziness going on, but they might not have really read anything until now, or paid attention to the candidates. They are NOT saturated in this like I am, for example. Maybe they do not know one cannot literally acid-wash emails -- for all they know, one can, who knows. Some might be even more uninformed and actually be ready to believe that Hillary has been fighting a less than 10 year old organization "all her adult life", even if she somehow is a co-founder of said org (huh?).
Sometimes fact-checking seems pointless, and it sure is if you pick the right scenario. That does not mean that it is without value.
But yes, "who fact-checks the fact-checkers" is a VERY relevant thing to keep in mind. Since this is all a bit new, maybe mechanisms (not necessarily tech) will pop out, or have already, to establish who is trustworthy (always under revision) and who is not, just like it is done with polling.