That might apply to any other ancient city, but my question regarding Jerusalem was predicated precisely on its unique status as Machane-Yisra'el. I'm guessing that in the wanderings in the Midbar people had to leave the camp to releave themselves, and since Jerusalem inherited the status of "the Encampment of Israel" then it would have inherited all the stringencies that went along with it.
Then maybe the Essenes were the official maintainers of the outhouse place. [Little humor there. That would have been a very long and anxious run for anyone in Jerusalem who had to go.]
Seriously, it is possible that people in Jerusalem went outside of the city. People who get plenty of exercise have that option (from experience as a soldier). Sedentary, contemporary people have more watery and unmanagable bowels.