I'm thinking along a different line. The Decatur office can have a passport ready in 5 days. So, if they travelled to Decatur on March 7th or 8th to bring the necessary documentation and then picked up the passport on their way out of the area on March 13th. The AA went out on the 14th, and although she was reported missing on the 13th, they could have reached Decatur before she was reported missing. All they needed is a notarized document with her father's signature. "If no parent is available to sign, the third-party in loco parentis must:
Appear with a notarized written statement or affidavit from both parents or custodial parent(s), authorizing the third-party to apply for passport. When the statement or affidavit is from only one parent, the third-party must present evidence of sole custody of the authorizing parent."
http://morgan.alacourt.gov/Pages/PassportsUnderAge.aspx Which is why I'm curious if the two had time to travel to Decatur together to get a passport before the March 13th abduction.