I don't think it's "narcissistic" to try to assess whether your prospective psychiatrist is well trained. "Prestige" is a loaded word, since it connotes snobbery, but, given that there are so few external markers for competence in psychiatry, I think one's training institutions are at least some measure of competence. And if I'm playing the odds, yes, I'd think that someone who graduated from the most famous residency program in a city is a better psychiatrist than someone who trained at a hospital renowned for its bad training, recurrent malpractice, and financial insolvency.
That's not to say I'd necessarily go looking for someone who trained at one of the places in the top 5 in US News. That might be easy in New York, Boston, or Baltimore, but there just aren't that many of them around the country. If I'm in Columbus, Ohio, I'd guess that the better psych graduates of OSU would be just as good as their east coast counterparts. Is Ohio State as famous in psychiatry as in football? Well, no, but I'd guess that most excellent future psychiatrists from Columbus will train in Columbus at OSU and I'd go by word of mouth. If, however, someone recommended a psychiatrist who trained at XXX (name a residency unloved by Ohioans), I'd probably assume something negative (he or she did badly at medical school; doesn't speak English; is problematic in some way) and steer clear. I can change my mind, and it's likely there are excellent graduates of XXX, but I don't see it as peevish to prefer the Ohio State grad (I'm using OSU as an example since I've never been to Columbus, Ohio).
I live in New York, however, and work at one of those prestige places, and so I do think about training sites when I refer patients. I know plenty of our graduates who are problematic, but it's never because they are stupid, ignorant of psychiatry, or slothful. It's always other stuff, and generally that other stuff is fairly easy to detect--and so, in the case of our grads, I can at least rule out some of the common causes of patient satisfaction. It's reminiscent of the situation at Ohio State, at least in regards to their football players. If I'm choosing up sides in a pick up football game, and someone is identified to me only as having recently been a cornerback for the Buckeyes, that guy is going first in my pick up draft; he may be a jerk, a bad team player, etc, but I will at least know that he's really athletic, and the other stuff will show itself quickly.
Oh, and my understanding of US News is that it is a voting contest, but it's not limited to academic psychiatrists and it has nothing officially to do with either residency training or research. It's a date-free vote on clinical reputation by psychiatrists around the country, which is probably why serious academic types roll their eyes at some of the names throughout the list--and certainly roll their eyes at the specific rankings throughout. At the same time, they do definitely care where their place is ranked (or unranked), partly because residency applicants use it as a criterion for matching.