yes, you are wrong. There are I believe 4 major schools of Sharia, which arose as judges interpreted the Koran and Hadith to apply it to specific cases. They disagree with each other in many ways, and each different interpretation is legally acceptable. These schools thus have a tradition of case law, which operates essentially the same way that American Anglo-Saxon law operates. This book covers the topic in considerable detail.

https://www.amazon.com/Misquoting-Muhammad-Challenge-Interpreting-Prophets/dp/17807478