This is an interpretation of a scene in Episode VII, but when Rey is informed by Han that she is in the Millennium Falcon, she makes mention of the Kessel Run. She overstated it (as 14 parsecs from memory, sorry I don't have the novelisation of the movie), but clearly she was impressed by this figure. Han corrected her to 12 parsecs by muttering it under his breath.
Han's claim of 12 parsecs seems to be accepted as widely-known fact, at least in the Outer Rim, who would likely have a fair idea of whether it sounded like bantha pudu. Even his correcting Rey's mistake back to the same figure some 30 years later gives credibility to his claims rather than it being simply an off-hand comment to impress an old man and a farm boy.
If you read the quote again:
The kid, like most people who heard the tale, looked impressed. The old man was not, however, “most people.”
There is no mention in that passage that Obi-Wan didn't believe it, merely that he didn't wasn't particularly impressed by it. Nowhere does it state that the tale wasn't true.