Poor women are far less likely to think about their own mental health, let alone admit that they have problems and go for treatments. So, it's not that rich women have more mental health problem than poor women, but rich women have the time, money and space to care about their mental health and seek help.
I have been seeing my grandmothers, aunts, my own mom... they have so much pressure in their lives that their mental scars are telling upon their health, but they simply don't have the money/ luxury to seek mental help.