The solution solves the exact issue. A claim of fact is sent from one party to another and the blockchain--which is independent of either party's trust--holds that claim including who it was sent from, when, and what the claim was. The only thing it has the potential to not solve is the possibility of the party lying in that claim.

In this specific example, what would they change to photo to? The case is to stop joyrides. Who would be able to take a joyride and end up with the odometer exactly as they had Photoshopped it to hours or days ago?

But yes, depending on the application, photos can be manipulated. But that is stating the problem with using photos, not the timestamping app.