I don't think it's the wealth, though. It's the person.
I think it's a question of the person managing the money, or the money managing the person. Those managed by their money are not responsible, no matter how far into the black they are financially. There's just so much more to being responsible than solvency.
Hmmm... I don't think I was clear enough giving just the one sentence out of context with the rest of the essay it came from.
The writer was talking about how obtaining wealth doesn't give you freedom. It isn't an end-point goal to obtain it and then consider yourself "comfortable." Obtaining wealth brings you responsibility- an obligation (probably a better word.) You are obiligated to use the money wisely, to "do good" with it.