He admitted to picking her up, therefore he is the last person to see her alive. He needs to prove he dropped her off where he said, the Feds don't need to prove he picked her up, they have a confession.
Are you saying that you believe that picking someone up and giving them a ride is kidnapping? No way.
He doesn't have to prove anything, he's innocent until proven guilty. The Feds have to prove that he picked her up with the intent to commit a crime. Simply giving someone a ride is not a crime.