The reason he said he went outside to watch the Presidential Parade was that he went outside to watch the Presidential Parade!
Now!
Here is Officer Baker in the Darnell film.
------------We see his ungloved right hand go to his hip holster as he runs
------------By the time he is reaching Mr Truly's position, his gun is in his hand
In a few seconds' time, Mr Oswald (Prayer Man) will find himself confronted by a gun-toting officer shouting 'Do you work here?'. The officer is looking for someone who works here so they can show him where the stairs are!
To anyone who-------------like Mr B. Lovelady--------------hasn't noticed Mr Oswald's (Prayer Man's) presence on the steps for the motorcade, this will look like Mr Oswald is being 'stopped' by the officer as he (Mr Oswald) is making his way out of the building!
And that's exactly how the incident-that-is-hardly-an-incident will be related to the press
by DPD later that day!