The "deal" that was cut with the 6 rescuees is probably one of silence. Oceanic probably already told the world that the plane was found in the ocean with everyone dead. The 6 are probably under orders not to tell anyone the truth.
There can't be silence if their identity as the "Oceanic Six" is known. It's public knowledge that they are the survivors, hence, everyone was not "found dead". So the "truth" about the island I agree is the reason for the silence, but anything about the crash, it's survivors (or it's non-survivors) is now public knowledge.