Some other things to keep in mind about the Tippit shooting:
-- When Mrs. Roberts last saw Oswald after he left the boarding house, he was standing near the street. She looked out the window a short time after Oswald left the house and saw him standing near the street, not speed-walking toward the Tippit scene.
-- Initially, the murder weapon was firmly identified as an automatic pistol, not Oswald's revolver. The person who identified the weapon as an automatic pistol was a Marine combat veteran and an experienced policeman, Sgt. Gerald Hill. Hill based his automatic-pistol identification on the shell casings. As any firearms expert can attest, it is very easy to distinguish between automatic shells and revolver shells. Additionally, in a 1986 interview, Hill said he knew the shells were .38-caliber shells because he picked one of them up and examined it. This is significant because .38 automatic shells are marked ".38 AUTO" on the bottom. Hill specifically said he looked on the bottom of the shell that he examined. It is no wonder, then, that Hill got on the radio and said, "the shells at the scene indicate that the suspect is armed with an automatic .38."
Standard ammo nomenclature puts the bullet caliber first followed by a description that identifies a specific cartridge. For instance, in .38 caliber, there is .38 Short Colt, .38 Long Colt, .38 Smith&Wesson, .38 Special, .38 Auto, .38 Super .38 Super Comp, .38 Casull, etc.
After it's introduction circa 1900, .38 Special has been almost ubiquitous for that caliber, to the point were just saying ".38" has become almost universally understood shorthand for ".38 special."
So when Hill says "The shells at the scene indicate that the suspect is armed with an automatic 38, rather than a pistol," it should really be read as "automatic .38 special."
Also, notice that he has to add "rather than a pistol" to indicate that the gun is a .38, but not the .38 that would be expected from his description of the shells.
One might argue that .38 special was designed for revolvers. This is true, but not the whole story. In the first decades after WW2, a number of automatic pistols were chambered in .38 special and became somewhat popular, especially among target shooters. The most famous of these is the S&W model 52.