I strongly suspect that the main reason the identification of Oswald was based on the "hairline" of the Prayer Man figure. A close-up of Darnell (taken from the Prayer Man website) reveals the figure does indeed appear to have a hairline similar to Oswald:

It must be noted that this picture is covered with "distortions", most probably a product of enhancement. These distortions are everywhere and consist of patches of horizontal lines close together. Look at Prayer Man's right elbow and you will see one very clearly. Note how it "drags" a darker colour into the elbow.
Now look at Prayer Man's head and you will see such a distortion. There is one that runs through the top of the head and carries on, cutting off the dark shadow of the door frame behind.
In the extreme close-up below this extended distortion is picked out with a red arrow:

Prayer Man's distinctive hairline is the product of distortions created by enhancing the picture.
It has nothing to do with Oswald's hairline.