I am delighted to find that there is information online that helps to understand this. (OK, perhaps it is more accurate to say that the information adds more complexity than clarity, but it still delights me).
Aside: @Jamesqf (et. al.) is quite correct to point out that the North American native population is diverse, and what holds true for the Lenape may not be true for other nations. (Given that the various tribes had very different economic and political bases, I'd be very skeptical of any answer that relied on (for example) Hopi or Dineh sources to predict Lenape behavior.) I have tried to limit my answer to what I know of the Lenape.
The Lenape had a culture in which the clan and family controlled property. Europeans often tried to contract for land with the tribal chiefs, confusing their culture with that of neighboring tribes such as the Iroquois. The Lenape would petition for grievances on the basis that not all their families had been recognized in the transaction (not that they wanted to "share" the land). Wikipedia:Lenape quoting American Anthropologist
It is also worth consulting the Walking Purchanse; my cursory analysis of this is that the lack of understanding (the frame challenge) had to do with the stakeholders, rather than the concept of property. The Lenape perceived "land ownership" as deriving from family groups, while the Europeans perceived land ownership as deriving from a government. The Lenape didn't have the same institution of "government" as the Europeans did, so even if the Europeans intended to approach the negotiation in good faith, the differences in assumptions doomed the negotiation.
I suspect that someone more skilled & knowledgeable than I could shed some light on the difference between property rights for objects & goods, & property rights for land - which is critical to a high quality answer to your question. Your original question included "market commerce", but that concept isn't relevant to the actual question, which had to do with land rights, so I omitted it for brevity.
Other thoughts, not fully developed into an answer
In my opinion, this question is a opportunity to examine the concept of property and the institutions of commerce in a pre-economic society. At least to my perception, @EmLi has phrased the question to invite a frame challenge, and an answer that included such concepts as potlach, Capital Deepening vs Organic composition of Capital, and exchange entitlements might be useful. (I can't find an easy explanation of exchange entitlements. From my very biased perspective, exchange entitlements are a horrific form of community repression, so I'm not the best person to summarize them)
The summary is that "property" is a complicated concept, with multiple interpretations. Our modern, capitalist, commercial definition of property is only one of a complex set of possible definitions. I'm told that in certain cultures, if you do not return a tool to its correct storage location, you lose "owernship" of that tool; in such cultures. Took me a long time to wrap my head around it. (I"m not citing the culture, because I don't trust my memory.)
@EmLi, I'm sorry I can't give a good answer to the question. Before I went any further, I'd need to watch the documentary and understand the context of the Lenape leader's statement. Was it factual or rhetorical? Any answer without that context is... suspect. I hope that what I've provided will at least give you some directions for research, and perhaps attract some commentary from people more knowledgeable than I.