Yes, they make a big deal about their "live studio audience", but that doesn't mean it isn't annoying as hell. In fact, I'd prefer it if they used a laugh track, because at least then they'd adjust it so it doesn't sound like a bunch of inebriated hyenas. Of course, just because they have an audience doesn't mean it isn't rigged:
A friend of mine has been to a taping of the show. They spend 20-30 minutes getting the audience ready with a stand-up comedian and other fluffers. Their whole purpose is to get the audience excited and in a laughing mood. They really pile on the hype about their laughter making the show successful and how important the reaction is. They talk about the microphones needing big loud laughs. Etc.
When the show finally starts filming, it's a rare scene that's filmed in one take. Therefore when the show is edited, they will independently choose the "best" laugh and use that for final take. In that sense they do use an edited laugh track, it's just one that's created by the current audience.
Then there's the dialog pacing, which is constructed to suit the exaggerated laughing instead of the comedy. This awkwardly false nature can be easily seen if you take away the laugh track or (less subtley) replace it with a caricature laugh. This is a problem with a lot of sitcoms, but Big Bang Theory seems to be especially bad.
Now take a look at John Cleese's approach on handling audience laughter while filming Fawlty Towers. Here's an example from A Room with a View. Compared to that, Big Bang Theory feels stilted and forced, while Fawlty Towers has a more natural rhythm that's so much easier to laugh at.
Of course, it also helps that Fawlty Towers had good writing and actually is funny. Two things Big Bang Theory can rarely claim.