The individual in ELK V. WILKINS doesn't meet that standard because, "he does not allege that the United States accepted his surrender, or that he has ever been naturalized, or taxed, or in any way recognized or treated as a citizen by the state or by the United States. Nor is it contended by his counsel that there is any statute or treaty that makes him a citizen." AND
"Under the Constitution of the United States as originally established, "Indians not taxed" were excluded from the persons according to whose numbers representatives and direct taxes were apportioned among the several states," http://supreme.justia.com/us/112/94/case.html
As the court mentioned in that case, Indian tribes are dealt with by treaty/legislation and their members have their own jurisdiction outside the taxing districts of the states. This has nothing to do with illegal aliens.
Ark has nothing to do with illegal aliens either.
His parents were legal, permanent residents.