One way to look at the Christmas story is to compare it to another story (Easter) in the same religion. The Easter story looks coherent even when the serial numbers are filed off. The experiment was done by C. S. Lewis, who was able to write a coherent story (The Lion, the Witch, and the Wardrobe) that included a disguised version of the Easter story. As far as I know, that hasn't been done for Christmas. This makes the Christmas story look less coherent.