What does veracity problem mean?

The phrase comes from a (possibly erroneous) Carl quote from that story about the supposedly crazy girl who they used to live with. Off the top of my head, the story that she told was that she gave Peter money to pay the bills or something, he assured her he did (he did not), but Carl warned her that Peter had “veracity problems” – that is to say, he doesn’t always tell the truth, lol. I have no idea if the story is actually true haha but I can hear Carl saying that in my head!