Unless Oswald was driven to the scene, it's hard to get him there in time on foot, especially since the evidence suggests the murder happened a few minutes earlier than the official story says.
Some interesting tidbits that should make you go hmmm....
8/19/66 Richard Stark and Paul-Michel Mielche said they were harassed and threatened in Dallas while working on documentary film Rush to Judgment. Police warned them "it might be dangerous" if they didn't get out of town. They said their impression was that the police â€œwere more concerned about our footage on the death of Tippit .. than in the Kennedy shooting.â€ (San Francisco Chronicle)
12/26/1963 FBI report: JIMMY EARL BURT said he drove his car to the next intersection which is Denver and 10th Streets and turned west on 10th. He immediately saw a police car parked at the curb in the middle of the block. It was parked facing east on 10th Street. A police officer was lying on the street near the left front wheel. BURT later recognized him as being an officer who frequented that neighborhood. This particular officer was known by the name "Friendly" to the residents of that area.
In his Warren Commission testimony Vol. 3 page 324-325 Scoggins gives some startling information about Tippit's activities. Tippit was observed in the neighborhood quite often: â€œI noticed he stopped down there, and I wasn't paying too much attention to the man, you see, just used to see him every day, but then I kind of looked down the street, saw this, someone, that looked to me like he was going west, now, I couldn't exactly say whether he was going west or was in the process of turning around, but he was facing west when I saw him.â€
Witness Virginia Davis also thought Tippit lived in the area:
Mr. BELIN. Where was the police car parked?
Mrs. DAVIS. It was parked between the hedge that marks the apartment house where he lives in and the house next door.
One press account from that day read, "Investigators said....'We have a report the fellow who did the shooting of the policeman had a rifle in a car with him.'" (Dallas Times Herald 11/22/1963)
WFAA-TV news coverage (sometime after 2pm on 11/22): photographer Ron Reiland is interviewed, just back from the Texas Theater. He says that the police officer was shot with a â€œ.38 automaticâ€¦200 or more police officers went into the Theater and found a man sitting in the second row from the back that was armed with a shotgun.â€ Crowd outside the theater was almost a lynch mob.
[Later WFAA-TV footage, unknown time, same day]: Reilandâ€™s film footage of a cop holding a discarded white jacket. Report that a man had come into the Theater â€œwith a shotgun over his arm, of course everybody broke and ranâ€¦â€ Police Capt Pat Gannaway is reported to have said that suspect worked in TSBD, had been in Russia, married to a Russian, and was the same man who shot Tippit.