I don't believe there is a percentage you have to be to "claim" a heritage, as many times, people favor physical features of one or two races over others. At some point, you have to realize that whatever racial background you have converges into a general breakdown of anglo vs. hispanic, african, asian, or Native Indian. Not that sub-categorical ethnicities are any less important, but they are simply a combination of one or more of the above larger ethnicities.
To answer your question about what to fill out on an application in order to get entitlement for a race...I see it as a matter of personal preference. Is that fair? Well, maybe not to everybody, but perhaps that's because people don't always take the time to explore their roots.
From my perspective, I have 5 or more heritages, with one that is literally a melting pot of most ethnicities combined in one loosely categorized group called "Anglo-Indian", to mean that my ancestors were of European and Portuguese descent and intermarried with Asian-Indian locals and created their own ethnicity. So what do I claim? I mean, I appear to look Indian to some, Portuguese to others, and yet there are those in my family who favor our German, Irish, Scottish, or English roots instead. It gets very confusing! And I think it all boils down to what YOU want to acknowledge, keeping in mind that all people no matter what color they are remain special, so there is no shame in any race. People should embrace each nationality for what they are, because ultimately they all tell a story...theirs and yours, no matter what percentage.