It's mostly because they want to use their jokes for a special down the road, but if someone records them during a smaller venue with the same jokes, it'll ruin the special.
Not to mention it could be a bit they're still working on and fleshing out, so not only will it be out there already but it will be a potentially subpar version of the bit.
I'd believe it. I love Chappelle's show and specials. I won't go see him live again though. I saw him once about 10 years ago and it was a big disappointment. He was very stoned, and the only interesting part was when he dressed down an audience member who kept yelling at him about Rick James.
Comedians tell jokes, they aren't news organizations that need to do fact checking.
And even if they did hold to that standard, what a crazy bad example to pick. He was correct. So you think he got 'caught' telling a joke that had true facts that hadn't been verified yet?