I will have to agree with your pediatrician
, that there probably was something in the toilet that caused this abnormal black oily substance.
This is easy to verify: if it is the toilet, every time she urinates in the toilet the black substance will appear, but if she pees in a cup, or maybe a different toilet, ti should be clear. In my almost 30 years in pediatric practice, I don't know of any disease that will make anyone urinate black oily substances. (But then again, I don't pretend to know everything!)
Keep observing and checking.