I have the natural right to beat up people smaller than I am. Its true; it is inherent in my nature and the laws of logic that people of lesser stature are inferior and meant to do what I say. Unless maybe they have a pointy stick or something
Rights as we know them are social constructs. People gotten as far as we have by moving away from such basic rights as the one I outlined above. However there's a right way to do things and there's a wrong way to do things and a society with some basic rights seems to be an inherent mathematical optimum for how to do things in a society. Are they natural rights because that's the best way to do things? Your definition calls for rights that inherent in the nature of living beings which depending on the spin you put on it may or may not be the same thing.
Rules can change and if they don't disaster is inevitable. Back in the day of black powder smoothbore firearms a right to bear arms was all well and good; one individual could not do much damage. Even a cannon would have made a mediocre terrorist weapon. In the days of tactical nukes even the NRA is not going to take that rule too far; there are some arms no sane person is going to let anybody buy.