Simple question for simple minds  

What you have provided is an example of a Dual Purpose flight. While you provided patrol services outbound, once you drop that crewmember, you have the provided transportation to that individual. 

Additionally, it doesn't matter what is being "paid for" or the operator chooses to classify the flight, "patrol" in your example. 

Finally, the FAA has provided the answer to this question via the Bonilla opinion referenced above. It only matters when they are notified.