Certainly, private individuals sometimes did and still do behave in the same immoral way.  However, many of them simply relied on the actions (or lack of action) by governments, and were quick to take advantage of an act of government usurpation.

In the Americas, the native inhabitants did not universally stand aside while their tribal or clan territories were encroached upon.  Quite often, they stood to defend boundaries which had been clearly defined and respected for generations. 

While their methods of defense where quite often brutal by our standards today, more often than not it was the power of an opposing government that stepped in (sending in the Cavalry) and simply brushed aside hundreds of years of established claim. 

Where agreements were made and treaties signed, those treaties were quite often simply disregarded by the governments making them, once it became convenient and expedient to do so.

A good example of proper (moral) behavior is said to have occurred when William Penn obtained a patent (title) on land in the New World, including much of what is now the Commonwealth of Pennsylvania.

William Penn purchased this patent from then-King James I for a substantial sum of money.

When the king asked Penn what he was going to do, Penn reportedly responded that he was going to the New World to deal with the proper owners of the land, the Indians.

True to his word, he did.  The result was that Pensylvania was a particularly peaceful area.  As long as Penn had anything to say in the matter, no single instance of an Indian-inspired uprising against the white settlers occurred.  Both Indians and the settlers respected the property claims of the other.