A better way to phrase this is that natural law (of rivalrous goods) is based on possession, not ownership. "Ownership" or property is a human invention.
When a lion possesses a carcass, the hyena's don't respect it's property rights, they respect it's possession (unless they can over take the possessor), but the lion cannot leave dozens of killed carcasses stored around for future use.
Our notions of capitalism are based on concepts of property rights which are human inventions. One could reasonably be expected to defend one's own immediate possessions, home, or farm, but the invention of property allows an individual to control a vast amount of possessions, backed up by the power of the state.
When free marketers say "capitalism is natural", I think what they're really saying, is that market forces are natural, and by that they mean, individuals have demands, and are willing to trade possessions for them, and do not need a state or other framework for this 'bottom up' system to work. But that's a gross simplification, by taking a huge mental leap from a barter economy on the small scale to a modern capitalist economy. The modern market of trade bears little resemblance to the small scale microcosm thought experiments.
Reality is, our modern system is based of hundreds of years of evolved civil institutions, common law, political structures. It's the reason why a 'free market' in some countries is a "failed state" of misery, and not a paradise.
All economic systems are "based on trade", since they are all mechanisms of arranging trade.
That doesn't make capitalism at all special among the universe of all actual (or possible) economic systems.