Chase, I thought I posted a responce to your question last night, but I must have pushed the wrong button since I don't see it this morning.
I asked my query after just finishing reading Mr. Harry Pfanz's "Gettysburg-The First Day". Mr. Pfanz's who is a former historian of the Gettysburg National Park used two sources to document this event.
He gives the name of the Confederate Lieutenant as Frank M. Harney (page 329-330) of the 14th North Carolina Infantry. Pfanz'z makes no mention as to why Lt. Harney in his dieing breath told his friends to send the flag to President Davis.
So I guess that we can only spectulate as to why Davis placed such a valued attachment on that Trophy.