This case seems to follow the dissent in Mitchell written by Justice Sotomayor. Justice Sotomayor emphasized two points, which are present in this week's case. First, she disagreed with the plurality for arguing and deciding an issue that was never briefed or argued by the State; namely, that exigent circumstances existed. Wisconsin had argued at trial that the implied-consent statute gave them consent to search the unconscious driver. Second, Justice Sotomayor emphasized that the new blanket rule from the plurality would shift the burden from the State to the defendant.
The plurality attempts to counter these two arguments by claiming first that the Wisconsin Supreme Court had actually brought up the issue of exigent circumstances (not just implied-consent). And second, that they are not shifting the burden because the plurality is not conceding that the State did prove there were exigent circumstances.
The second point seems to be contradicted by the actual plurality holding, which sent the case back to trial court for the defendant to make a showing. And this is exactly what the SC Supreme Court was alluding to when they departed ways with the plurality in Mitchell.