Largely correct, but I'm a hopeless pedant: strictly speaking, a local oscillator is not necessary. Simple AM receivers, back in the day, didn't have them. For anything else, and definitely for GPS, it's largely theoretically, but I couldn't let it go...

Incidentally (to add something of value to this comment ) radar detectors (for detecting police speed-traps) are typically heterodyne, and simple ones are usually very noisy. So much so that (at least in states where they are illegal) police often use radar-detector-detectors to pick them up. Of course, those are also heterodyne receivers, so some motorists use radar-detector-detector-detectors to shut their radar detector down (and warn them) when they detect a radar-detector-detector...

Electrical engineering (combined with government regulation) is almost as good a racket as being an impartial arms merchant.