If the person gives permission for a search, then the cops can search. In this case:
“A records check revealed no problems with the documents, and Darisse gave Vasquez the warning ticket. But Darisse had become suspicious during the course of the stop—Vasquez appeared nervous, Heien remained lying down the entire time, and the two gave inconsistent answers about their destination. Darisse asked Vasquez if he would be willing to answer some questions. Vasquez assented, and Darisse asked whether the men were transporting various types of contraband. Told no, Darisse asked whether he could search the Escort. Vasquez said he had no objection, but told Darisse he should ask Heien, because Heien owned the car. Heien gave his consent, and Darisse, aided by a fellow officer who had since arrived, began a thorough search of the vehicle.”
http://www.supremecourt.gov/opinions/14pdf/13-604_ec8f.pdf
Ah, well that makes more sense. The idiot brought it on himself then by surrendering his rights.
Ah, so the truth comes to light.... As I suspected, the court ruled properly... the owners gave consent, in doing so no 4th amendment protection was violated.....Sotomayor showed just how much of a complete idiot, and completely unqualified jurist she is once again, she did not protect anything, but was the voice of uneducated blather.