I interpret it as meaning that its hard to be virtuous when you are dependent on an income. Not impossible of course, but made more difficult by being dependent on an outside income. I think the Greeks recognized, what is still true today, that people who are dependent on an income source, other than their own, are more susceptible to manipulation (i.e. doing things that may not be virtuous because you need the income) or being prevented from doing something virtuous because it would threaten your source of income.
When you are financially independent, you are free from those types of outside manipulations where the carrot is often times money or an income. You can be truly virtuous, even in the face of adversity, because your livelihood isn't threatened by someone pulling the plug on your income. I think one type of example is, for instance, having a Supreme Court where there is a life-time appointment. The theory behind it, at least, is that when you don't have to fear losing your job (or your income) you can be truly non-biased and independent. I put an emphasis on theory here of course..
I feel like I see similar sentiments here on the forums, as people start to get closer to FI. People seem to be much more likely to speak their mind at work, argue for what they think is the right thing to do, and simply walk away from their income if need be.