You are correct. It takes the concurrence of four of the nine Justices to “grant cert” (allow an appeal to proceed to oral arguments). There were not four Justices who wanted to grant cert to Barnett v Obama therefore the lower court’s ruling which dismissed the lawsuit stands.
Judge Carter dismissed the suit. He denied a motion for reconsideration. He denied a motion to transfer the case. He denied a second motion for reconsideration.
The plaintiffs then appealed to the 9th Circuit Court of Appeals who affirmed the lower court’s dismissal. The plaintiffs’ motion for rehearing was denied. A request for an emergency Writ of Mandamus to allow inspection of Obama’s original birth certificate was denied. A second request for a rehearing was denied. A request for a rehearing “en banc” ( by the full court rather than a three judge panel) was denied.
The plaintiffs then appealed to SCOTUS where the Petition for a Writ of Certiorari was denied.
I think Cruz has the right Idea. Make these bastards stand for election every six years. We can get rid of the really stupid ones pretty quickly after that.