The short answer is no.
The longer answer is complicated.
Over the last year, I've had more candidates ask me this than I had in the previous several years combined. I suspect it's a function of the abruptly-worse job market, in which people who might have been shoo-ins in the past unexpectedly fall short. I've heard it asked out of apparently sincere bafflement, in an I'm-trying-to-trip-you-up tone, and in indignant anger. I can't answer any of them.
I hate the question, because it's one of those times when the ethical impulse and the legal impulse conflict. As much as I'd like to answer the question in some cases, there's nothing to be gained for the college by doing it, and potentially a lot to lose. So I fall back on something like "it was a very strong pool," which is true but not revealing (or helpful).
Ideally, I'd be able to say things like "your answer to x suggested that you're settling for this job, and other candidates seemed actually to want it," or "you didn't really answer question x." But it's hard to know where an answer will go once it's given. Someone who is honestly looking for tips to improve might decide later that the reason given sounded discriminatory, and will use those words against the college. Or, she might try to argue the points, and you don't want to get sucked into that conversation. (I learned in my teen years that you can't argue your way out of "dumped.") Every statement you elaborate can, and may, be used against you in court.
Although there have been times when I wished I could have shared some pointers, at the end of the day the question is lawsuit bait. "The committee thought another candidate had more range." Well, was the range desired indicated in the ad? If not, is it a pretext? "We went with an internal candidate." So the search was never really valid in the first place? "It really came down to fit." So you don't hire my kind? "One member of the committee hated you." So much for confidentiality...
I could try to dodge any sinister readings by simply piling on the negativity, but there's such a thing as adding insult to injury. And much of the time, it wouldn't be true. Typically, everyone who makes it to the finalist stage is strong, and I have to admit that many cases come down to degrees of excellence or who better complements the department as it's currently composed. Losing doesn't mean you're a loser.
Then there's the epistemological issue. Decisions made by committee can be hard to pin down to clear reasons. Why did the 3-2 vote go the way it did? Legal scholars make careers trying to suss out the real reasons behind 5-4 Supreme Court decisions, and they at least have the advantage of having written opinions to parse. I can theorize as to why someone on a committee voted the way she did, but if pushed, I'd have to admit that it's mostly speculation. And anyone who has served on a contentious committee can attest that the results of votes can be surprising. Committee deliberations can go in unanticipated directions, and group dynamics take on lives of their own. Attributing a committee decision to a single post-hoc reason is usually reductive at best, if not simply arrogant. And getting sued over a speculative post-hoc statement that wasn't even accurate is a colossal waste of resources.
None of this is terribly helpful to spurned candidates; I get that. Making it to the finalist stage, and then getting shot down without a reason given, can be frustrating. (I've been there.) But most of the time, it's the least-bad response to a difficult situation.
Wise and worldly readers, have you seen (or received) an answer that actually helped?