Actually, Post #19 is the key, IMHO.
But....we know how the USSC is stacked, right now, and there has been a concerted effort since the beginning to avoid the Issue, at all costs, to stifle a confrontation there.
If Arizona took the case directly to the SCOTUS under original jurisdiction then arguably Sotomayor and Kagan would have to recuse themselves as a decision for ineligibility would nullify their appointments. ;-)