Wait, what was that middle thing again?
Yes, it turns out that the Dutch expedition led by Peter Minuit actually purchased Manhattan from the Canarsie Indians, who were based out of Long Island. They only used the island of Manhattan as a convenient place to get shitfaced, and were by no means the rightful owners (that would be the Manhattoes). So when a bunch of surly Dutch traders showed up and offered to buy the place, the drunken Canarsies readily accepted. Basically it was an old-school version of the "Wanna buy the Brooklyn Bridge?" scam--except this one actually worked.
So the whole situation is less like a crafty white guy buying a gold mine for a pittance from some poor, suffering widow, than it is a quasi-retarded white guy wandering by a bar and offering to buy it--cash in advance of course--from the first drunk he sees passed out in the gutter out front. On the down side, this was still a s****y deal for the Manhattoes, who presumably came by the next day and wondered who the dickheads moving into their houses were. But on the upside, it was a pretty fantastic night for the Canarsies, who got history-altering wasted and somehow came out of the whole thing a grand richer.
Well, until white people murdered them too. Then it was pretty much all square.