There was a common conception for many years in Western society that it was the only true "civilization." In fact, when I attended High School (in the dark ages) the World History course that was taught was in fact Western Civilization. When one combines the obvious Social Darwinism with the fact that western society is primarily Christian and overtly missionary, one can understand how people of the West considered it their duty to "civilize" people from other cultures. A classic example of this is Rudyard Kipling's White Man's Burden. Another classic example is from an old hymn I often quote to my students entitled "The Kingdom is Coming:"
From all the dark places of earth's heathen races,
Oh see how the dark shadows fly.
The voice of salvation unto every nation
Come over and help us we cry.
The "come over and help us" is from a passage in the New Testament. It also appeared on the coat of arms for the Massachusetts Bay Company with a picture of an American Indian.
The zeal of Western society to "civilize" the rest of the world has resulted in the destruction of many elements of native civilizations, which has been a tremendous loss. One need only consider the destruction of Aztec and Inca relics by over zealous priests; the Anglicanization of India and Europeanization of many parts of Africa. The West has imposed its own value system on other areas to the manifest detriment of their own culture and society for purely selfish reasons.
I would argue that they do not, but that is simply a matter of opinion.
In the place where I grew up, the native society was largely poor in material terms. However, the society had always been that way and the cultural attitudes of the people and their customs were adapted to this state of material affairs. Because of this, you could argue that they were "well off" because their culture and their circumstances matched.
During the time that I lived there, Western media messages and Western economic expectations had diffused to where I was living and had been embraced by many of the people. Many became "better off" in material terms as they came to have cars, TVs, and imported foods. However, the coming of these material goods and the expectations that were part of a Western economic system did a great deal to alter the culture. This led in many places to a large increase in youth suicides as people were unable to cope with being pulled towards Western economic attitudes while, at the same time, being pulled in the opposite direction towards traditional attitudes.
In this sense, native societies can be less "well-off" in social or cultural terms even as they improve their economic status.