How does this handle anonymous sources?

Not only do you have to account for what those sources say, but also, a reporter reporting what an anonymous source said can be 100% factual (Yes, the anonymous, valid source was indeed reported accurately), but maybe the anonymous source is incorrect. The reporting is accurate. The source is not.

Basically, a lot of grey area. And with that comes the issue of anything not "fact checked" by a service like this could be dismissed. What harm does that do?

Not a dismissal of a service like this. Rather, just open questions.