Actually I remember the Lucas story the same way you told it, except I've never seen anything that says it's in the script. I first read it in the letters page of the Marvel Comics adaptation of the original movie. Some readers were complaining about the parsec thing. The editors quoted Lucas (who had already come up with this response for someone else) as saying that Han is the sort of bull artist who doesn't always know what he's talking about.
That's my original source for it too. But I think I've seen something more recently that showed the script reference.
From the Wookieepedia page on the Kessel Run
In the revised fourth draft of A New Hope in 1976, the description for "Kessel Run" is put as follows:
It's the ship that made the Kessel run in less than twelve parsecs! Ben reacts to Solo's stupid attempt to impress them with obvious misinformation.
So it implies that the puzzling speech of Han Solo is "misinformation" and not truth, and it has nothing to do with the nature of the Kessel Run in any respect. Han means nothing other than impressing Obi-Wan and Luke with pure boasting. Indeed, even in the final version of the script, the parentheses attached to Han's line state that he is "obviously lying."
Which is ambiguous, admittedly; it could either mean that he isn't using "parsecs" correctly or that they know it's impossible for the ship to perform as well as he claims. So it's inconclusive.
It goes on to say:
In the commentary for Star Wars: Episode IV A New Hope DVD, George Lucas mentions that the parsecs are due to the Millennium Falcon's advanced navigational computer rather than its engines, so the navicomputer would calculate much faster routes than other ships could.
So in this case, it would seem that it's Lucas's claim that it really does
make sense that's the revisionist explanation, and the original intention was that it didn't make sense (in one way or another).