How much an individual earns and how much an individual saves are both separate and related issues. It is absolutely possible for a person living in poverty to save money. Though that previous statement is an oxymoron (save money while in poverty), it is possible through discipline, lowering one's standard of living, etc.
They are related because there is a definite correlation between how much a person earns and how much much they save. How? Financial literacy. The more people earn, the more people seek knowledge regarding finances. Poor people do not see the need to learn or practice saving, investing, etc.
Lastly, I say this with all due respect, but you obviously have not been poor or associate with poor people closely and regularly. I remember my mom deciding between the light bill and food. I see patients skip getting their prescription filled because rent is due. There are more people like this than not. Just because you do not see does not mean it does not exist.
We have a lack of sympathy in our society due to the inability to empathize.