Amazing! I also had exactly the same experience that led me to research this a few years ago, realizing that: - GPS works even in airplane mode (while on a literal airplane) - It works without cell service, or wifi, or anything - The United States of America controls the GPS constellation, and they can (and have!) turned off GPS off certain regions at will when necessary (which has prompted other countries to launch…
They do send a location - to be more exact, they send rough locations of all satellites in the constellation (almanac) and precise location of themselves (ephemeris). Devices like mobile phones, however, usually get that data from other sources because it's much faster than listening to data over GPS.