This boils down the to the following. First, the police would have believed that any discarded wallet found at the crime scene would have been linked to the shooting. Second, the name associated with the wallet owner would have immediately been broadcast as a potential suspect in the murder. We know the latter didn't happen. What does that tell us? That the "wallet" was not found at the scene. Whatever it is, the police know the owner is not a suspect. That leaves a witness wallet or Tippit's citation book.
So it's your belief that Agent Barrett and Officer Croy were mistaken?
They very well may have been mistaken but nevertheless, we're stuck with two conflicting accounts of where the Dallas PD gained custody of Oswald's wallet.
Based on the available information, neither of us can conclusively say they were mistaken or lied.