Could be any of those. "Rich" is able to live comfortably with no financial stress. For some that is a small home in a village somewhere off the grid spending their days fishing. For others it is millions of dollars. But generally, I think if you have a couple hundred grand in the bank you're rich.
People who live off the grid also live off the grid during a disaster such as Japan's tsunami. So there is the same trouble from lacking during a disaster as there is in this independence you connect to riches.