It doesn't matter.

AA was not the operating carrier of the onward segment and a BP is not alone good enough to board the onward segment (because the onward carrier will check docs as well).

Any Passport Agency can issue a passport in a few weekday hours when the time constraints are there. If OP's relative had the proper documents with her, she might have postponed for a day, headed into LA and camped out at the Passport Agency . All presuming that the next day was not a weekend and that it was a US passport.