No one has ever found the document Hawthorne says was an outline of his "Romance" and most critics do not believe that there ever was such an outline. Why do you think Hawthorne might have made this up?
First, let's identify that the purpose of this question is to make a statement responding to the prompt of what may have motivated Hawthorne to make up a story about a lost document which outlined his novel.
Let's differentiate that the narrator of "The Custom House", the preamble to the novel that mentions this document, from Hawthorne. The narrator of "The Custom House" is meant to mirror Hawthorne in terms of both supposedly telling a story about their Puritan ancestors. However, the story is still meant to be fictional, as is the document in question, which alludes to it.
This being said, Hawthorne adds the touch of the "lost document" to add a dimension of realism to the tale, and to attempt to bridge the story from fantasy to reality. Similarly, the mirror narrator wants to bridge his "Scarlet Letter" story to a dimension of reality with the comment:
What I contend for is the authenticity of the outline.
Therefore, in a way that mirrors other works such as Don Quijote de la Mancha the author will use the device of a mirror narrator, a mirror story line, and an element of "the real world" to blend the real and the fictional and make it more believable, more relevant and meaningful to the reader.