Not necessarily.

Every country to which I've been -- and I've been to India way more than most people -- has a way for people to exit the airport and still stay in the country even after having cleared departure immigration control minutes or even hours earlier.

On one more than one occasion -- especially during the late November- early March period -- after having cleared departure passport control at DEL, I and the other passengers have had to exit the DEL airport and wait to take a flight 12+ hours later -- especially during the November-March period. In other words, there is a way that this can be done without leaving the country.

International travel or not, Indian airports are not well-designed for passengers in the airports to exit the terminal prior to departure. India actually has rules that even restrict domestic passengers from exiting the airport after having entered the terminal building. Those same restrictions apply also to international passengers, including international transit passengers. Welcome to the bizarre world of Indian "security", "bureaucracy" and "politics" -- a world I know way, way too well. A lot of this junk in India that frustrated the OP's exit from DEL airport and return landside started because officials didn't want people coming into the terminal to say goodbye to departing friends/family/colleagues/others and crowding up the airports.

DEL is just worse than even LHR T5 when it comes to wanting to get back landside after having gone airside.