I've always had doubts about Reid's account and the notion that Oswald would go out the front door. She didn't know him at the time. She described him as being dressed only in a white t-shirt which seems extremely unlikely. She may have talked to others before giving her account of events as I seem to recall someone referencing her saying that Oswald had lunch with Truly. So she had clearly talked with others in the immediate aftermath of the assassination and got certain details about the lunchroom scrambled while knowing that Oswald had been in the lunchroom with Truly (but not understanding this was a brief, chance encounter). She then wills herself into history by claiming to have seen Oswald around that location.
The problem with this, Mr Smith, is that Mrs Reid could not possibly have believed that Mr Truly had been lunching with Mr Oswald when the police officer burst in
-----------she (along with Mr Ochus V. Campbell) had just been standing
beside Mr Truly watching the motorcade...
But you're quite right to doubt Mrs Reid's cockamamie story!