Rational reporting points out that the decision was made on the basis of federal supremacy in election law for federal elections.
Irrational - i.e. Leftist race baiting - reporting is calling it a defeat for an "anti-Latino immigrant" law (that from the Anti-Defamation League, who I suppose are worried about the millions and millions of Jewish Mexicans who will be deprived of um..something...can't quite figure it out).
The fact is that the AZ legislature can narrow the requirement to State elections, but that will be a bit difficult logistically since federal/state election ballots are usually conjoined.