One of the things I've learned is that pursuing the truth often isn't worth it. For instance, if I have two friends and A tells me one story and B tells me a different story, one of them must be lying. My natural instinct is to talk with A and B individually to try to discern who is telling the truth and who is lying. Generally, such probing questions make the questionee suspicious -- to some degree -- and both A and B find out that they've been telling different stories. And I get caught in the middle.
Therefore, my new policy is that I segregate information and don't try to discover the truth for its own sake. If the issue at hand is itself important then I'll try to figure out what's really going on, but if it doesn't involve me and (therefore) isn't important, I'll just let it slide. I'll think about how the stories may reconcile and try to figure out what the real truth is, but I won't rock the boat by probing. It's just not worth it. Plus, it's gossip.
Assuming A and B's stories are mutually contradictory, it only follows that one of them is wrong, not that he's lying.
I think the best thing to do in such circumstances is get A and B together, and let them both explain to each other (and you) the situation in their terms, and the truth will eventually sift out.
This is how Presidential debates ought to work. Unfortunately.......