Amy Farrah Fowler pointed out:
“Indiana Jones plays no role in the outcome of the story. If he weren’t in the film, it would turn out exactly the same… If he weren’t in the movie, the Nazis would still have found the Ark, taken it to the island, opened it up, and all died, just like they did.”
Here’s a decent rebuttal:
Once it becomes inevitable that the Ark should be removed from its resting place, the only suitable ending is for it to wind up in another resting place where it will never again be disturbed. And it never would have made it to the unnamed warehouse without the efforts of the redoubtable Dr. Jones.
Source: http://ordinary-gentlemen.com/2013/10/19/the-big-bang-theory-gets-it-wrong/
He figured that they were digging in the wrong place. Also, they followed him to Marion in Tibet, where that one doctor burned his hand on that staff head.