Possibly the most plausible explanation I've heard for the blatant error in unit in the cantina scene in A New Hope is, according to a copy of the script, Skywalker and Kenobi were supposed to react as if they knew they were being fed a load of hogwash — an emotion that was, unfortunately, never really conveyed.
The Wookieepedia article on the Kessel Run mentions this, plus another explanation offered by George Lucas in DVD commentary (that he meant his navigation computer could find shorter — and therefore faster — routes), but only as "behind the scenes". The more prominent explanation is given thus:
Solo was not referring directly to his ship's speed when he made this claim. Instead, he was referring to the shorter route he was able to travel by skirting the nearby Maw black hole cluster, thus making the run in under the standard distance. However, parsec relates to time in that a shorter distance equals a shorter time at the same speed. By moving closer to the black holes, Solo managed to cut the distance down to about 11.5 parsecs.
Essentially, his ship was so fast, he was able to take a more dangerous shortcut.
Why do I think this is a load of bunk, in the context of the cantina scene? The whole conversation at that point was about speed. Why mention distance when your client is asking about speed? Expecting a farmboy and a nomad to know the details about a particular space race as a condition for winning a fare seems like pretty bad business sense. Solo may have made some bad decisions, but I don't see him as being entirely stupid.
If you do take the Wookieepedia explanation as fact, though, it does explain that awkward silence with the following deleted scene:
Han: "It's the ship that made the Kessel Run in less than 12 parsecs."
Luke: "So, that would mean he'd have to take the Maw shortcut? How fast do you have to go to get around there?"
Ben: "Um, let's see, take a left at Geonosis Prime, you'd have to circle Kamino..."
Luke: "No, Kamino's too far; that's at least half a parsec out of the way; he'd have to go past Denobula."
Ben: "Denobula? Oh, yeah, at the Circle-K. Used to love their donuts. I haven't had their donuts since, oh, before you were born..."
Luke: "So, to get down to 12 parsecs, you'd have to cut pretty close to Naboo in order to make that turn."
Ben: "That would put you within... ten million kilometers of Maw?"
Luke: *scribbling* "No, no, carry the 4."
Ben: "Oh, right, right, half a million kilometers. Now, with the mass of Maw, the velocity needed for a Corellian freighter to escape would be... um..."
Han, annoyed, impatient: *ahem* "She's fast enough for you, old man."
Assuming Han was full of it, though, and Ben and Luke eventually caught on, I imagine the scene in docking bay 94 might've played out a little differently...
Luke: "What a piece of junk!"
Han: "She'll make .5 past light speed."
Luke: "What, .5 parsecs?"
Han: "She may not look like much, but she's got it where it counts."
Luke: "Really? Does it count all the way to blue?"
Han: "I've made a lot of special modifications myself."
Ben: "Yeah, like the ability to tell time with a ruler."
Han: "But, we're a little rushed..."
Luke: "Yeah, we've got to go in just a few inches."
Han: *thinking* I should've let Greedo shoot first...