I have no problem charging private entities rent for the appropriation of natural resources. What I have a problem with is demanding a share of the private property that they fashion out of those natural resources. From a public standpoint, it should make no difference if someone appropriates a ton of iron ore and places it in their living room as a collector's item, or if they use it to create a supercomputer. They should pay the same fee to the public in both cases, since it is the natural resource usage that should be charged, (and that the public has a legitimate right to charge a fee for), and not their private actions upon that material. But current tax laws, and Proudhon's argument which the parent comment cites, delegitimizes the value that one adds in the process of creating the latter.
Before your body was formed, there was no "you", so the concept of ownership didn't apply. The "offender" in that case was the laws of physics, or some deity if you prefer.
We can play your game the other direction. If using "practically free" natural resources doesn't deprive you of your rights, you would have no objections to a company rolling into your neighborhood with bulldozers and taking all of the nutrient-rich soil so that they can turn it into something highly valuable and sell it to other people. You would have no objection to a company like Nestle claiming ownership of a local river and prohibiting nearby residents from drinking from it.