Spoiler How does the ending prove?
Sorry Please don't attack, I am serious. How did finding the treasure prove his family was not behind the lincoln assassination?
shareI believe that since they found the tresure based upon the clues found on that page (and the adjoining page),that the names there were NOT as co-conspirators of the plan to kill Lincoln, rather they were there because of the hiding of the treasure.
shareThis is a weak point in the plot, but Mitch Wilkinson says in the end that he framed the Gates ancestor to get the Gates family involved in the treasure hunt. I presume from that either it was he who wrote the names on the missing page, or that the Gates ancestor's inclusion was a code-breaker, not as part of the assassination. The other names were, however, part of the assassination.
Gates family's motivation, however, is that they want to prove the family story is correct. They firstly prove that there was a coded message in the diary and secondly that this leads to treasure. The Gates ancestor therefore tried to destroy the page to protect the treasure from the Confederates, not to cover up his part in the plot against Lincoln. Finding the City of Gold, however, only corroborates the story: it doesn't conclusively prove his innocence.