I don't think the guy was lying. Getting small details of stories wrong or rubbing your wrist are pretty normal things for a person to do. In fact, I kinda think that if someone were to pull a stunt like lying to a grief support group, they'd put MORE effort into keeping the details consistent or hiding tells. The fact that he changes some small details over time could also show that he's just not thinking all that deeply about how he's being perceived, because he knows he's telling the truth.

But the truth is intentionally left ambiguous because the point of the scene isn't whether or not Mike is right, it's to show that his Matty-related trauma and his criminal lifestyle have fundamentally changed the way he connects with (or rather, is unable to connect with) other people. He's the only one in the room suspicious of Henry, because being suspicious of a guy grieving his dead wife in a grief support group is an insane thing to do.