I don't have any hard evidence, and when you're looking at something like PhD programs in psychology, where theoretically the biggest factor that gets you in is "fit" it's hard to make generalizations. I'd be lying if I told you that I thought race/ethnicity and gender meant nothing at every program. I think you have to look at a program and its recent history. If every year, a program gets qualified applicants from a diverse pool, and every year it's 7 white women between the ages of 24 and 27 who get in and nobody else, at some point, people will start asking questions.
The problem (if it's a problem) is when you're dealing with "fit," once you hit the basic quantitative requirements (GPA, GRE scores, acceptable LOR, a well written SOP), everyone's theoretically on an equal playing field. You could be picking the white guy because you want more white guys in the program, or because he's the best "fit." Who can say otherwise? If you're writing something on a dry-erase board, and you open up a pack of new markers, it may mean something that you chose the blue one, or it could just mean you just needed a marker that wasn't out of ink.
Remember, this isn't law school. You can't look at all the accepted students and say well, if the standardized test score is X points or less lower than the other accepted students, we can still tip the scales for them if they're of R race or G gender or S sexual orientation or O country of Origin, and easily be called on it. In psych, the Caucasian man with the 1550 GREs and 3.97 GPA with three publications on eating disorders could lose out to the Latina with a 1250 and 3.68. Was it racial? Sexist? Not if the Latina is interested in PTSD and has worked in a VA hospital on the topic, the faculty member she applied to was taking students and the one the guy applied to wasn't.
I'm a white man, straight, married, nearing 31, committed childfree, vegetarian, child of an immigrant. Did any of those demographic characteristics help me to get into my program this year? Hurt me in getting into others? Who knows? I was the only guy in the interview stage for my program. Everyone else interviewing was extremely well-qualified. I consider myself extremely well-qualified. Maybe they wanted to have men represented in the incoming class. Maybe my research matched up better with faculty. Maybe my name was the one drawn out of the hat.
But, to answer your question, psychbiker, yeah, I'd check the "other" box. A lot of times, the question is just for reporting aggregate applicant data to the feds or the university, or for fellowship/scholarship opportunities.