Writing a joke is hard work. Sure, it's 140 characters, but it can take a long time of searching out inspiration, research, and then writing and rewriting to get it in its punchiest form. Most of us come up with good ones on our own every once in a while, but producing enough to sustain an online following can be a heavy investment. It's no surprise the producers are leaning on twitter for some protection of their reputation and/or livelihood.
As usual, though, it is misguided. The difference between a successful joke and a failed jokes is precisely that the former is likely to get repeated. It's half the reason people follow this accounts and watch comedians is so they can borrow material to entertain their friends and romantic interests. Maybe that's not 100% honest but that's a part of what's driving your traffic. Some jokes have to be told from your perspective -- a citation ruins the humor. (Or you've modified it and citing now would be entirely honest.) Sometimes you remember the joke but not where it came from. That's part of the life of a joke.
But it is strikingly dishonest when you have other accounts stealing material wholesale, morning radio programs running your material without credit, and traffic-generating pages copying it verbatim (except for the citation). Whether that should invite legal response I don't know, but it should certainly invite some shame.