Basically, you’re correct, like a lot of things in golf, it’s based on the honor system, players turn in their scores that get calculated and produce a handicap, the scores that get turned are accepted as accurate and the player has followed the rules of golf.
If one person plays by PGA tour rules and another maybe doesn’t then their handicaps are not true reflections of their playing ability.
Is there such a thing as a “minus handicap”, sorry I don’t know the correct term.