I don't think rights are naturally occuring.
I disagree entirely with you here.
Sans a society of any kind, I can say whatever I want.
I can defend myself however I please.
I can live.
I can worship whoever I wish.
I can be around whoever I wish.
These things are inherent things I can simply do, not granted to be by any individual or society, but simply are. They the extent that I am able to do them myself.
Now, individuals may attempt to stop me from doing those things. They may attempt to keep me from exercising those rights. But they can not take those rights away from me permanently, short of death. If someone caught me in the wild, kept me in a cage, and bound my mouth....if I somehow escaped and was on my own, I could still live where I want, eat what I want, say what I want, all up to the capacity that I myself can make it happen, because they can't actually remove those rights from my person. They are inherent.
The problem is that, in nature, there is no notion that one's right's end where another's begin. I have a right to protect myself and to live somewhere. Another person has a right to eat and to live as well. That person may very well want to live where I live. He's well within his natural rights to take my land, and I'm well within my natural rights to defend myself and stop him from doing that.
As such, we enter into societies through a social contract. There's two ways this typically happens. Either we as a people CHOOSE to enter it, or an individual/group has enough power to FORCE us to enter it. Once entered it, that social contract establishes how those individual natural rights are protected/restricted and potentially works to create other, governmental rights (which, unlike natural rights, are not inherent but dependent on the social contract).
I can say what I want, worship who I want, live where I want, eat what I want, be around who I want in nature without the support or framework of any government. Those rights are inherent naturally.