It has to be per story without party bias. It's a really hard problem to solve.
I've thought the same thing, but the people interested in using such an extension would get their news from places other than Facebook.
Self-selection bias greatly reduces the efficacy of such an extension.
They could get their news from Facebook too, they would just more likely subscribe to more reputable pages and have less hoax-sharing friends.
Then they would claim that reputable sources too are biased against their beliefs and they'll come up with their reputable sources. Paranoia is some people nurse and profit from—unfortunately.