Patient has positive urine bilirubin test indicating that he has water soluble bilirubin accumulating in his body that has already been metabolized by UDP-glucuronosyltransferase. In order for water soluble bilirubin to be accumulating in his body there must be defective excretion of such bilirubin. The only option available that matches such is "obstruction of the bile duct".
why hemolysis is wrong:
There should almost never be straight up bilirubin in the urine. In hemolysis, the excess bilirubin is excreted in the bile. After bacterial conversion and reuptake, some will be excreted in the urine as urobilin. However, in obstructive disorders, the conjugated bilirubin will never have the opportunity to undergo bacterial conversion to sterco/urobilin. In this way, the conjugated bilirubin has no other way to be excreted other than directly in the urine.
credits to /u/alacran763 on reddit
i think this is because bilirubin is a soluble liver breakdown product of heme, but has not entered the intestine/colon for gut bacteria conversion to stercobilin or urobilin. urobilin in urine is normal.