Can't answer the question because I don't know enough of the specific programs. Just wanted to back what Golfpropsyche said regarding social workers. Some programs expect the psyche residents to take up this particular duty that psyche nurses or social workers often do.
While doing this does help you to learn, if you're doing it as a resident, all the time, everyday, its really just robbing you of your time and its not really what I'd call "true" psychiatry.
Yes, calling up places for disposition & insurance companies is a learning experience that improves your clinical skills & helps you to understand the often times unfair reality of turfing & billing but the lesson is learned fairly quickly (maybe a few weeks, tops). Then after that its just scutwork, and very frustrating work at that. I've seen some cases where residents were doing it for hours a day for years depending on the program. Some programs expect residents to do this because they're trying to save money on social workers--so they'll dump it on the lower class citizens of the medical world-the resident.
I'd certainly consider this factor when applying to a program. I'd aim for a program that doesn't make residents do this work. If you are fortunate to get into one that doesn't push this on residents (I'm in one that doesn't--thankfully!), at least be in good communication with your social workers about this so you as a doc can learn this process through osmosis. Maybe sit in on a few sessions where they do call up the insurance companies and other institutions for open spots.