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.
Sure it is. If someone steals your gold, you can call the people with guns to arrest them and get it back to you (often). It doesn't have to work 100% of the time to be an effective deterrent.
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.
I'm not aware of any way to actually increase the total amount of real gold in/on the earth in any meaningful way in an ECONOMICAL matter (i.e. you have a net positive income from producing it). The government can make more REAL MONEY for far less than the value of the money.