Hi, yes I have extensive experience with that program. I worked as a post-bac IRTA fellow at the NIH in Bethesda after college and before med school. During my time there, I also shadowed doctors at the Clinical Center. One of them was William Gahl, MD, PhD, who is the head of the Undiagnosed Disease Program at NIH, among the many other things he is responsible for. He is a renowned physician, and you can read about him in the links below (one of them talks about his similarities to "House").
I used to attend his conference on Thursday mornings with his research and clinical fellows, where they'd review the current patients they have admitted in the wards of the Clinical Center. There were residents and medical students there, too. The med students there happened to be from Duke, spending their "scholastic year" doing research under him or another related lab. After that, we would all go to the wards for bedside rounds to check on each patient. He is a great doctor, very friendly and personable. The other doctors in the team were friendly, too. All of them are very excited about teaching. I remember that even though I was not a med student, they were very inviting and encouraged me to join them in their bedside rounds and Dr. Gahl would point out various physical manifestations of the rare diseases he studied on the patients and would bring the med students close to the patient to examine it. Then we'd go outside the room and discuss the patient and look at any relevant film or discuss their pulmonary function tests (since many of the patients had Hermansky-Pudlak syndrome). Very fond memories for me! Certainly it had an impact on my desire to practice medicine in an academic setting.
Anyway, he is the person to contact, and all his info is in the second link. The Undiag Dis Program works such that any patient can be referred to it, both from within other clinics at the NIH or outside the NIH. Coincidentally, I was shadowing a neurologist at the NIH during his moving disorder clinic and he and his fellows came across a patient with an undiagnosed disease and decided to refer the pt to Dr. Gahl's program. Very, very fascinating stuff and academically stimulating, to say the least.
Hope this helps.
http://www.cnn.com/2009/HEALTH/02/03/undiagnosed.diseases/index.html
http://www.genome.gov/10005723