Well, if LE says they can verify his story, then I would guess they can. Who knows? I can think of several ways. For one, what if he took Katelin and actually had someone else with them. Maybe he has a gf or something. Maybe they stopped to eat something even pick up somehitng from a drive-thru and were spotted somewhere in Spotsy on the way. He could have used a credit card, they asked the restaurant employee and they say yes those three people where in the car. Then they have traffic cams of his car in the area of the mall. LE says that the place where he says he dropped her has no cameras. So he and his gf (or whoever) drop her off and then minutes later they are on camera somewhere without her. Who knows.... wandering the aisles of Best Buy or something. So that tells LE that she was with him at x-oclock and then minutes later she is not. Maybe LE doesn't want to bring in all this info about the SD and another person because people would go crazy harassing them and accusing them of killing her. So they know he is innocent and that is all they will say.
Just one scenario that would fit, imo.
ETA: I almost forgot to add that LE also is under no obligation to divulge any of that info with the public. They don't have to tell us how they know. They don't even have to tell the family. Anyone who has been close to a missing person case knows this: Family is often as much in the dark as the general public. Unless LE wants the world to know, they won't even tell family because chances are that someone will slip and blab and that could destroy progress in the investigation.
