One key element -- It has been demonstrated [in this thread] that Johnny Brewer could not possibly have heard about the shooting of a local policeman on the radio before 1:30PM Dallas time. Such a broadcast was not made until after Oswald was actually confronted in the Texas Theater. The Brewer story is just one example of the fake news surrounding the assassination.
Where did Brewer say he heard the announcement before 1:30?
From what I've read he gave no time - approximate or otherwise - as to when he heard it on the radio. My mistake: He told the 6th Floor Museum in an interview that he said he heard about the shooting of an officer BEFORE Oswald showed up in front of the store. That was, if I have it right, about 1:36. So he would have heard a broadcast report about a shooting before that time.
Myers says that KBOX made an announcement at about 1:31 that an officer was killed. Oswald was arrested in the theater at approximately 1:52. That is the time when Sgt. Hill radioed in that a suspect was apprehended.
Radio transcript is here:
http://mcadams.posc.mu.edu/dpdtapes/tapes3.htm