Absolutely correct information would be nice but almost as good is flawed information that has a known amount of error. The census isn't going to contradict anyone, or prosecute anyone, but they can sample the population and make their own estimations. Of course you can also control for errors in your estimators by having them estimate the race of a known sample. The end result is you get a raw result with a well defined error. Which, in the end, is about as good as it gets.

Yes, some people are going to lie on purpose. You are also going to get a percentage who just, for some unknown reason, check the wrong box. There are even a small percentage of people who lie, but end up telling the truth. A considerable number of people misunderstand their own ancestry. A good percentage, largely out of wishful thinking and cultural idealization, claim American indian ancestry. Must of us are mutts. That is a good thing. Mutts are usually healthier and better adapted than purebreds.