There were hoaxers and pranksters in every era, and some of them have left documents behind that in later days seem realistic. Anyway, whether there was a secret mission or not it's unlikely that a determined naval historian would find no record of the building and commissioning of said "U.S.S. Minuteman". In the year cited Decatur was entering the final year of his term on the Navy Commission, and was already known nationally for his feats in the two Barbary wars and the 1812 spat. The assignment seems out of line with where he was in his career at that time, though I have no doubt he remained an adventurous guy.
Whoever it was, we all know he did not kill a pregnant Jersey Devil that crashed through the roof and dispatched a midshipman.
One of my favorite Jersey Devil legends, and I do think there is some kind of veracity to the claim. I’m not sure where Madison lies in all of this however, if at all. We do know that the event would have had to have been sometime in 1819 when Decatur was indeed in NJ testing the quality of cannonballs from Batsto and Hanover. Earlier claimed time frames just don’t jive well because of his service in the Barbary wars and the most absurd 1778…..the year he was born. While it is true that Decatur was a celebrated hero by 1819, let us not so easily disregard the importance of munition production in this time frame, I don't think it would have been "below him' to be involved in this, especially with adventuresome nature thats always seems to be attributed him. The bottom line question I suppose is if Dr. James Killian accompanied Decatur, and if so, was it at the bequest of Madison. I have not seen the documents in question, but if the owner wants to prove their veracity a handwriting study should be done as well as a paper quality test. A fantastic wrinkle to the legend methinks, I’d love to see the document owners perform some sound scientific study to see if the event did actually occur as the legend suggest.