Elections are run by the states, not by the federal government. Also, even in a shutdown some level of spending continues.

FWIW, I’ve heard this statistic before as “Only 1% of Americans today are Native Americans” which feels a bit closer, though a quick Google indicates puts that number closer to 3%. That fact sort of inherently rejects the 99% claim, which indicates to me it may be exaggerated or has been repeated in slight error.