So, i'm no expert on colonisation of the Americas. However, i can give some insight into questions of property and sovereignty. The question of property and colonisation is pretty difficult and touches on the origins of the concepts of property and how different cultures view property.

I suspect this will not be a satisfactory answer, as it relates mostly to historiography and legal methodology, rather than the details of American colonialism. But the premise in you and your friends disagreement seems to be that a modern (lockean) notion of property is what defines a right, and even more, what defines morality. I will try to offer some insight and nuance in how modern law and traditional law interacts, what property and rights actually are and challenges in clarifying who has rights.

I will primarily talk about property and not sovereignty even if these are related and intertwined. Most of the problems described here for property, are true for sovereignty as well.

The problem of modern property rights and traditional culture

Initially, and generally, we can say that all humans rely on some form of relationship with natural resources or geographical areas for their sustenance, through various different social, economic and geographical conditions.

However, modern property rights are heavily influenced by Lockean notions of property, and we are to a degree socialised into such a view of property. A common belief at the time of early NA colonization was that no sense of property ownership existed for the native americans, and that they just wasted away the land. To quote Locke:

he who appropriates land to himself by labour, does not lessen but increase the common stock of mankind. (...) For i ask whether in the wild woods and uncultivated wast of America left to Nature, without any improvement, tillage or husbandry, a thousand acres will yield the needy and wretched inhabitants as many conveniences in life as ten acres of equally fertile land doe in Devonshire where they are all cultivated. (...)

Thus in the beginning all the World was American, and more so than it is now; for no such thing as Money was any where known. Find out something that hath the Use and Value of Money amongst his Neighbours, you shall see the same Man will begin presently to enlarge his Possessions.

Firstly it should be said here that Locke is absolutely wrong and has basically no idea how native american cultures and their relations to property work, nor their trade or commerce,

Secondly, he only really recognises a right to the land if it is done in the precise manner that land rights at the time were acquired in England, by labour and cultivation and enclosing the commons. Possession by cultivation became the key definition of property.

This evolved into more structured forms later, where property rights were tied to capital and written records of ownership. Thus property became written and formal. But property was still an either/or, a question of who had the right. This was in contrast to many other forms of legal systems that recognised many variations of a right to use only or various conceptions of collective property rights, or temporary rights, or juxtapositions of all these, instead of the more total and individual ownership tied to more intensive use. Patrick Glenn has a summary of how some traditional notions of property typically work:

the use of land consisted of communal or collective enjoyment, with no formal concept concept of property crystallizing this loose relationship between groups of people and the soil upon which they lived. Chiefs could allocate land for individual use without disruption of the communal holding, and with no "tragedy of the commons" through overuse.

This isn't a description of "no claims" or "no rights", it's a description of a system of custom and morality with defined notions on how things are typically used, who decides, who gets to use what. it's just one that is markedly different from the one we would find in Lockes England. These more limited or different forms of rights typically went unrecognised as they simply didn't fit the understanding of what property was

A good example of this is that because native-americans had a different definition and idea of property, they saw some early trading of property to colonisers not as a permanent arrangement, but a temporary one. The English however interpreted it in their frame of unalienable and forever-lasting property rights and saw themselves as buying land rights.

So the key point here is to realise that all cultures had some notion of their relationship with things, with resources and with geography. When very different notions clash, one would simply not understand the other. That doesn't mean either of the cultural conceptions of property or rights are illegitimate, rather they are different systems adapted to different places and ways of life.

It should be said that concepts similar to what Glenn describes have typically existed in western legal systems as well, like the Allemend, a communal pasture, in Swiss law. Similar concepts of area-based grazing rights, or even literal property rights and economic rights, have always been a huge part of Norwegian law, especially in the north. The Norwegian Allemannsretten is also interesting, as a public and common right to a limited usage of nature. So these allemend communal pastures or the allemannsrett to nature doesn't meant these areas aren't claimed, rather, they are non-individual property rights. A right to usage held in collective by a certain group or everyone.

It however took western legal systems quite a long time to recognise the non-lockean concepts of property existing in other cultures, even if they had their own such ideas.

Continued below