Real answer: your race is self-declared. Other than Native American (which is tribal membership, not race), you are whatever race you claim to be. Just pick one for all of your documents. So, as long as they have been claiming it for everything, anyone who checks the box is honest.
The reason: There is no test for race.
For the most part, that is true. However, there are four caveats: the 1/16th rule, your employment records, your school records and other government info, like, birth certificate.
What did your parents indicate on your certificate? Now, the absence of a URM indication on the certificate would not, in itself, be incriminating, b/c some people find out about their heritage long after they're born. Many "Whites" are completely unaware that they are Black or Indian...or Mexican. Funny...some of them actually hate ethnic minorities, too. That's a cruel joke God plays on these White people, but that's another topic. lol!
Technically, in order to be considered Black/African-American, non-Hispanic (for example), one would need at least one parent to have been 1/8th Black, thus, one grandparent 1/4, one great-grand parent 1/2 and one great-great grandparent full Black. If a school or the bar wanted to delve into this, it could ask for family records (believe it or not, I have the actual slave records for my family, as do many Blacks). But, as is the case with a birth certificate, the inability to produce a family tree or other record would not necessarily make you a liar.
On the other hand, the school or bar could then ask how you came to know you were "part Black" and interview your other family members. I don't know if they'd go through the trouble of doing it.
More likely than any other available investigation method, they could look at your employment and school records, something the schools and bar might realistically be relied upon to do if they smelled a rat. They could check to see whether you have always indicated your status as a URM. Some state bars will pobably go back through EVERY job you have had and every school you've ever attended, according to what I am learning. If they were to find inconsistencies, they could bust you that way. But, as long as family members vouched for you, I don't think it would do anything but slow down your inevitable bar admission...unless you are just flat-out busted in a lie somehow.