Then you get sued for discrimination.
White people need to start checking the "Native American" box. Many already are and I don't blame them.
Eventually businesses will look to simply avoid hiring certain minorities, while rolling out the red carpet for others. A lot of dark-skinned Asians from India or Pakistan have wised up to this ruse and check the "black" box. And seeing how many of them are as black as the last banana, who's to tell them they can't?