The logic the majority used in ruling on this case seems pretty simple (unless I'm totally off): the patent troll had a patent that was still legally valid because there had been no court challenge to declare it invalid. Because the patent was still legally valid, the infringement of the patent is still a valid cause of action in a lawsuit.
Scalia's logic is that you can bypass a legal challenge over a patent that might be ruled invalid in court because it was never valid in the first place. The question is, though, how would you know whether the patent is valid without the court saying so?
But there are two separate types of infringement at issue here. First is direct infringement. This occurs when the defendant actually violated the patent him or herself. This is a strict liability offense, meaning that it doesn't matter if the defendant was aware of the patent or not, and it doesn't matter if the defendant was aware that his or her actions infringed the patent or not. And if the patent has not been declared invalid, it is presumed valid and the defendant is liable for damages even if the patent is later ruled invalid. This is well-established law and is not at issue in the Supreme Court's decision.
The other type of infringement is induced infringement. This occurs, for example when a defendant sells a product which would cause the end users to violate the patent. The defendant is not violating the patent directly. According to patent law, for a defendant to be liable for induced infringement, he or she must be aware of the patent and also aware that the usage of the product would be a violation of that patent. So the question before the Supreme Court was in the case of induced infringement, what if the defendant had a good faith reason to believe the patent to be invalid? I tend to agree with the majority here: if the patent wasn't declared invalid by a court, the usage of product would be infringing, so the defendant must have known that such usage would be infringing, since they knew of the patent. The dissenters (Scalia and Ch. J. Roberts) thought otherwise: if a patent is invalid, how can the defendant believe it to be infringed?