Warren: the problem with Brennan's testimony is that his original description doesn't quite fit Oswald in age and size: "“I could see the large red brick building across the street from where I was sitting. I take this building across the street to be about 7 stories anyway in the east end of the building and the second row of windows from the top I saw a man in this window. I had seen him before the President’s car arrived. He was just sitting up there looking down apparantly [sic] waiting for the same thing I was to see the President. I did not notice anything unusual about this man. He was a white man in his early 30’s, slender, nice looking, slender and would weigh about 165 to 175 pounds. He had on light colored clothing but definately [sic] not a suit. I proceeded to watch the President’s car … I heard what I thought was a back fire … I looked up at the building. I then saw this man I have described in the window and he was taking aim with a high powered rifle. I could see all of the barrel of the gun. I do not know if it had a scope on it or not. I was looking at the man in this window at the time of the last explosion. Then this man let the gun down to his side and stepped down out of sight. He did not seem to be in any hurry. I could see this man from about his belt up. There was nothing unusual about him at all in appearance. I believe that I could identify this man if I ever saw him again.""
After the Tippit shooting, a description of Oswald came out, it was noticed that the description of the man who shot the police officer was very similar to the description given after the president was shot. After the shooting Oswald fled and was later captured in a nearby movie theater. Later the same evening Brennan identified Oswald in a police lineup as the person who most closely resembled the man in the window, but Brennan said he was unable to make a positive identification. A few hours prior to seeing the line-up, Brennan had observed a picture of Oswald on television. Brennan attributed this to part of the reason he felt he could not make a positive identification, he did not want the image to have impacted his decision. On December 17, 1963, he told the FBI that he was sure that Oswald was the rifleman he had seen in the window.
Several months later, he also testified to the Warren Commission. During the extensive questioning, Brennan stated that at the time of the lineup, he believed the assassination was part of a conspiracy, and he was afraid for the safety of himself and his family. Because Brennan declined to make a positive identification in the police lineup, the commission regarded Brennan's subsequent testimony (that he sincerely believed he saw Oswald), as probative but not conclusive evidence that Oswald was the gunman in the sixth-floor window.
There's two possibilities beside what he stated: Brennan may have been influenced by later reports, or his memory and initial impressions were correct. I lean toward the latter, but cannot totally dismiss the former.