No, state courts are not federal courts. They ruled on a lawsuit saying Obama had improperly been placed on the ballot, and ruled IAW SCOTUS arguments and rulings.
The Supreme Court could have taken a case before Obama was sworn in, but declined to do so.
I would also note that any state legislature COULD pass a law defining NBC as requiring 2 citizen parents, and that would force a court case - but no state legislature will do so. Ever wonder why?
So you’re going to ignore the Arizona House’s attempt to make candidates (not just Mr. Obama, but all of them) to prove their eligibility for the White House.