Agreed. Cover. But kinda far fetched, that the doctor wasn't the one providing first aid to the survivors.
I'm guessing they made a deal with whoever perpetrated the cover up plane wreckage. Perhaps the same cabal owns Oceanic, and the big payoffs were part of the deal.
Chances are that the cover story has Claire one of the 8 who survived, but probably also saying she died, but not before making Kate promise to raise Aaron. The world would know that Aaron couldn't possibly be Aaron's mother, as everyone knew she was not pregnant and in handcuffs on the plane. The other person who survived the crash but died later is, obviously, the marshall, as Jack said on the stand.