Supposedly, Rookstool has a copy of a frame of the Reiland film where Croy wrote something about being the guy who "found Oswald's wallet." But Rookstool never quotes Croy as saying that Croy found any Oswald or Hidell ID. Rookstool certainly would have done so had Croy said it himself. Dale Myers interviewed Croy several years before Rookstool, and Myers says that Croy never mentioned anything about finding Oswald or Hidell IDs. So, did Croy know on 11/22 that the wallet was Oswald's? Or did Rookstool present his matching-wallet-flap spiel to an aged Croy who simply went with what he was presented, just like John Stringer did with John Canal's presentation.
FWIW, Ron Reiland said on 11/22/63 that the wallet was Tippit's "billfold". However, he's wrong about a number of details about the crime, so I can't see this statement being definitive in and of itself. Then again Reiland was at the scene filming the Police going through the billfold/wallet/notebook/coffeemaker, and his statement was recorded contemporaneously with the events.
You do understand that you've confirmed that Croy and Reiland agreed with Barrett's statement that their was a wallet found at the Tippit scene, right?
The fact that Croy did not mention the Oswald and Hidell ID's doesn't negate that. Reiland saying that it was Tippit's wallet (which we know from Marie Tippit) it wasn't also does not mean there was no wallet.
So, now we have three people who confirm the presence of a wallet at the Tippit scene.
I bring up the question of, did Westbrook ask anyone else (including and especially the radio dispatcher) about Oswald/Hidell because it's hard to believe that Westbrook would have asked only Barrett, given the situation. Further, if Westbrook didn't know whether the supposed "Oswald/Hidell" was a bystander, why would he not try to find out who this bystander might be? This of course would involve asking the bystanders at the scene if they were or knew Oswald or Hidell.
Who says that Westbrook didn't ask the bystanders if somebody had lost a wallet? No need to name any names. In fact, it would be wise to withhold the names just in case somebody came forward. He could ask that person for his name and check with the content of the wallet.
As for informing the dispatcher, they didn't even bother to put a description of the killer on the radio, which would have been a lot more effective than broadcasting a name. So, that's a moot point.