Imo, the whole McWatters episode is with some other man, and somebody convinced McWatters that if must have been Oswald, when the "ticket" was presented with a punch mark. (but no fingerprints of either Oswald or McWatters!?)
They wanted to make it seem as though Oswald was "in a hurry" and anxious, impatient, desperate to return to his boarding ASAP.
But Whaley contradicts that narrative, by having observed that Oswald just appeared to be walking normally and even offered the cab to a woman 1st.