I don't think it necessarily means all the justice of the Supreme Court opposed it. I think it means that fewer than four justices - the minimum needed - agreed to take the case up.
This was an application for a stay of the lower court’s order. Any single Justice can grant a stay. Justice Alito denied it first then submitted it to the other Justices, which is standard practice. None of the others granted the stay.
It takes four Justices to grant a petition for a writ of certiorari which means moving an appeal to oral arguments before the full court.