Somebody was wearing a jacket. There's no good reason to think that it was the same guy Brewer saw.
Many witnesses positively identified Oswald in the vicinity of Tenth and Patton, running with a gun in his hands and wearing a jacket.
Brewer saw a guy, who he said was Oswald, without a jacket.
Each of us can, on our own, choose to determine how much credibility to give these witnesses. Some can accept the obvious, that the witnesses near Tenth and Patton saw the same man that Brewer saw. Others can jump through any hoop that they have to in order to place guilt on anyone other than the actual cop-killer.