“Somebody on that show likes Palin. I suspect it might be Conan himself.”
I’d say Conan wants her on his show regularly. He is a tight ratings race with Letterman, and a few appearances by Palin would see him move ahead, perhaps permanently.
The enemy of my enemy is my friend. Letterman is so identified at this point with panning Palin that it’s a no-brainer for Conan to play at least a little to the pro-Palin crowd.
Oh, and vice versa: it’s a good move on Palin’s part to foster at least a welcoming relationship on Conan’s show.
Not only does she get a swat in at Letterman and his ratings every time she appears, but she provides an incentive for Conan to treat her fairly—which gives her a valuable late-night platform.