That's not enough. Your analysis is far too simplistic.
Let's say that man in your hypothetical who laid claim to otherwise uninhabited land has a son. The man dies, and bequeaths the land to his son. His son sails off from Greenland to Iceland for many years because, you know, those names are really reversed.
Another completely unrelated man comes to the land, where there is no one for many miles around, finds the land uninhabited and claims the otherwise uninhabited land as his own.
The son returns to Greenland, finds this new man on the land his father bequeathed, and says "Hey Squatter, get off my land!"
The second man says "I claimed this land, and I demand you recognize my natural right to it!"
Who owns the land? Is the newcomer a squatter or rightful owner?
How does the son enforce his right to inheritance, and who is to say the second man who has lived on the land for many years has no right to that land?
Of course it was simplistic, illustrations usually are.
Remember that in the simple scenario, the original man put up a fence, denoted ownership of the land. Thus the squatter would know that the land is claimed.
Clearly, as more people inhabit an area, the need for a resolution of disputes arises, which is why people develop laws and courts to adjudicate said disputes.
That we have laws and courts does not mean that rights are derived from them - quite the opposite, the courts are there to protect rights by providing a peaceful means to resolve disputes.
Joe has a goat, Fred gets a spear and holds it to the throat of Joe and takes the goat. Joe goes to court and the court rules that the goat belongs to Joe.
Did the court give the goat to Joe?
No, the court merely acknowledge the existing possession. This is the reality of rights, a just society acknowledges that we have natural rights, to life, liberty, and property. They do not grant these rights, but acknowledge and protect them. Locke said these rights rights came from God, Madison stated our creator, either way, the reality is that the rights are independent of rulers and governments.