The 1977 novel (before the movie) says "timeunits" instead of parsecs, which puts the "it was a distance of the run" argument to bed, at least for author's intent.
However, the first published script for the movie, from 1979 says "parsecs" but immediately says "Ben reacts to Solo's stupid attempt to impress them with obvious misinformation". There's some dispute about whether that was actually in the shooting scripts, which have leaked since, dated 1976, however the original scripts were heavily marked with penciled-in direction and stuff since they were constantly being rejiggered and stuff, so it's perfectly possible some additional direction was penciled-into the early typed scripts, and only for the relevant person, Alec Guinness. Remember this was before word processing was a thing, so you just manually penciled notes in.
However, you can check for yourself with the
actual footage showing Obi-Wans reaction to the claim. It's about 15-20 second in here, so just go from the top. Notice that after Solo's claim, Obi Wans eyes widen for a split second then he does a little sudden squint, like he's mulled over what was said and immediately going "hang on, wtf does that even mean?"
However, this is
still compatible with the later "parsecs measures how short the run was" idea, though Obi Wan's doubting reaction can still work with that. Han
could have meant that he shaved distance off the route, meaning he's a good pilot who'll get you there quicker, while Obi Wan didn't know what he meant, so is like "is this guy for real?" The fact that Obi Wan still went with Han Solo however, even with the possibly false bragging, is that he could
sense Han Solo was a good guy.