The two are not mutually exclusive. Gold, for example, is not backed by people with guns. However a financial and legal system can be built on top of it, in fact it was build on top of it until 50 years ago.
However fiat money must be protected by people with guns against forgery. With one exception: people in power are allowed to counterfeit it, thus robbing the common people, under protection of people with guns.
Gold and Bitcoin are immune to both types of forgery.
You only get a net positive income for producing gold if the price is higher than the cost of production.