After reviewing the Statute in question and the relevant CFR's, I've come to the conclusion that only a higher authority within the State or the Federal Election Commission has standing to sue for relief (Since I'm not an attorney, I could very well be wrong).
That seems to be my impression as well. It is not that the SCOTUS said everything happening was good but that the proper protocol in filing suit was not followed.
The meat of the matter, possibly hundreds of thousands of false voter registrations, is troubling to say the least but certainly not new. Remember the great quote from Chicago, "Vote Early, Vote Often." Bottom line is we as a nation need to do something to address voter fraud. Sadly I doubt it will happen.