Ah, this Falcon talk is bringing me back. If the Falcon is in it, it could be that Anakin made the Kessel run in it during the Clone Wars, and nobody has ever beaten his time. At the time, you see, he was a navigator on a spice freighter out of Kessel. Of course, it wasn't named the Millennium Falcon back then, and it had a different owner. But Obi-wan puts this info together in the cantina in ANH, and his knowing smiles upon hearing this information and seeing the ship that Anakin flew before he knew him tell us all we need to know.
That's the Star Trek Into Darkness approach to writing the movie, I guess.