I don't know why you're talking about the paper trail when I was clearly talking about the DNA aspect of it.
With two Kit numbers, and GEDmatch member can punch the numbers in and see that yes, the two people have a certain match of a certain size, at a certain place on a chromosome. Without that, it's "the honors system" not much different than a family legend, or some such thing. How do we know the person making the claim didn't make some questionable assumption, or simply a mistake (like even a typo)? How can we look into it, without the Kit number? Go through their whole list?