These days there is so much statutory law in the developed world that this distinction is fading away. Yes, it’s technically possible for a common law court to grant a new form of relief that isn’t derived from legislation or binding precedent (eg. the Mabo decision in Australia), but these days the common law is really a ‘god of the gaps,’ and if the courts aren’t satisfied with the common law remedies available 200 years ago or created later by statute, they have very little power to create new remedies. Of course, written laws are always open to interpretation in both the common and civil law system, and that’s what happened in this case (the written law being the U.S. Constitution).