As a student, it appears that colleges, universities, etc. get around this by "reporting" this info to the government. I have no idea why the school or government needs to know my 4 race makeup, but they call the shots and I am but a lowly student hoping to better myself.
The race question is NOT only asked of those in need of financial aid of any sort. When I started school I paid out of pocket and was STILL asked. Many schools still ask for race on their applications. Scholarships, grants, etc. also ask for this info, many are BASED on race or religious affiliation to the frustration of students of ALL races that otherwise meet or exceed the requirements.
Also, these questions often encourage incorrect answers because these forms often don't take into account the growing melting pot the world has become. Wherever this "data" is going, this is one reason that the data is wrong. A person can be equally mixed 4, 6, 8, or more ways but they are still often prompted or verbally told to "check one."