This is not something that happens miraculously. It is a misconception that some people are just inherently stingy and others are generous. Even if you want to be generous, everyone hears that little voice when you are giving, asking, "What if... [my house burns down/I lose my job/the car breaks down/etc].... and I need some saved money?" So it is evident it is a matter of training. Alhumdulillah, the Shariah establishes an ingenious training regimen that can train the human being to become generous if they follow it. And that is the difference between a society like that of Umar's Madinah and today's America. The human beings are the same, just they have not trained themselves properly.