There's an ounce of truth in this myth, but it's mostly a pile of rubbish. Most native groups did consider themselves administrators of their lands, and disputes frequently arose between them (as with other groups) when things were not done as they desired. For instance, it was understood that building a house on wompanoag land meant adhering to the wompanoag leadership. Hunting and grazing on another group's territory without permission was frowned upon. Early natives were generally tolerant of white settlers, and many customs prescribed the generous treatment of guests, but they did not see them as having authority unless it was agreed upon.

When settlers arrived in the northeast, many of the native groups there had already been greatly reduced by smallpox and other diseases brought by various explorers and fishermen up and down the coast. The Pilgrims in particular settled in land which had been recently forsaken, when over 90% of the patuxet tribe had died a few years earlier, and they detail a number of unoccupied dwellings and unclaimed foodstores, helping give rise to the belief that the Natives were more loose about ownership than was ever true.

Many of the property issues that arose between settlers and native stemmed from inconsistent logic on behalf of the europeans. By their definition, fenced-in land was intended for settlers, while woodlands remained with the natives, which both parties were fine with. But white men would hunt game in the woodlands, which natives saw as disingenuous, and they would allow their cattle to stray into the woods, which was highly destructive. They compared loose cattle breaking things apart, wrecking traps and footpaths and clearing brush (which scattered the various birds and small game living there), to their coming into the fields and turning over crops, breaking gates, etc. Originally on friendly terms, the settlers were inclined to agree with this reasoning, but the first solution (allow the natives to hunt straying cattle) was unthinkable, and the second solution (keep cattle fenced at all times) was highly impractical, leading to an uncomfortable and non-functional series of compromises. A smallpox epidemic came through, wiping out many of the prominent natives and severely reducing the original settlers.

The natives grew bitter at this and the settlers were greatly replenished in numbers with unsympathetic newcomers, leading to increased tensions. The natives, believing that the settlers had overstepped their bounds and claimed unfair privileges, demanded the reduction of settlements and the removal of white settlers from traditional lands, insisting that the whites remain in the outskirts and forsaken areas that they had originally been given. This did not happen, and the result of the failed negotiations was King Philip's War, one of the most horrific wars ever fought on the continent (in terms of population percentages) - a war waged by Natives over their perception of property. They destroyed over 80% of the new towns, and spared only what they perceived as "rightful" settlements (providence proper, newport and western mass) - a policy which ultimately led to their downfall, as the settlers fortified these towns and used them as bases for a series of counter-offensives that would nearly exterminate the remaining natives. All subsequent conflicts initiated by or against native powers (where they were key belligerents, and not merely allies) were over who had a right to live where.

*TL,DR *: the natives did not practice personal ownership of land within a tribe, but very much believed in land ownership, and fought in many bloody conflicts over land ownership.