Boundaries aren't arbitrary. The population is defined as the "City Proper". The official boundary of Tokyo ends where the next municipality (prefecture) starts, and has for eons been the boundary of the 23 wards of the old city, and that has a population of 14million. I'm not sure if you've ever seen any government ever, but they don't take kindly to the neighbouring one suddenly reclassifying an area as theirs so these are clearly defined (people know who sends them a bill for taxes).
Maybe you're confusing the words "greater area" which is a non-official designation that usually includes connected surrounding municipalities and in some cases conurbations from a whole extra city. The only time "Tokyo" has ever had a population above 14million is when talking about "The Greater Tokyo Area" which in Japan is the region of Kant and includes 6 other prefectures, Chiba, Gunma, Ibaraki, Kanagawa, Saitama, and Tochigi which all have their own governments and their own official populations.
No, these boundaries are not arbitrarily redrawn. Redrawing city boundaries takes a lot of effort from official acts of government, yes even in the 3rd world. - Again people tend to know when someone different comes asking for money claiming "you are mine now". It is public and doesn't happen very often.