You're in between a rock and hard place. Is it possible for you to speak with your counselor (you two are attending MC sessions, right?) in order for the C to open up a discussion about the importance of total honesty?

But I still don't buy his story, but what am I to do? How do you call someone a liar when he swears it is the truth?

OK, so his story doesn't fly, yet there's enough to suggest he's not trying to hide activities, but rather, just doesn't want to make this call into an issue. Let's assume that's what it is for now. Being watchful, you'll determine sooner or later if this is a correct premise or not, that's about all you can do. Just file the information for now.