The idiom "Rob Peter to pay Paul" is fairly well known and most people understand it to mean solving one problem by causing another. In many cases, people use it to mean paying a debt by incurring another debt. Here are some examples:
...to discharge one debt by incurring another (http://www.phrases.org.uk/meanings/rob-peter-to-pay-paul.html)
Why borrow money to pay your bills? That's just robbing Peter to pay Paul. (http://idioms.thefreedictionary.com/rob+Peter+to+pay+Paul)
Jacob: I think I'm going to apply for another credit card so I can pay off some of my bills.
David: Robbing Peter to pay Paul, eh?! Just be carful not to get into debt. (http://www.urbandictionary.com/define.php?term=Robbing%20Peter%20to%20pay%20Paul)
For example, They took out a second mortgage on their house so they could buy a condo in Florida--they're robbing Peter to pay Paul. (http://www.answers.com/topic/rob-peter-to-pay-paul)
We all get what these examples are trying to say, but they are not a completely accurate use of the idiom. Imagine robbing a bank to get money to pay your bills. If you get away with it, you're out of debt and you've solved your financial problem. If you don't get away with it, you go to jail. You could say that you've incurred a social debt, or you could imagine monetary fines being assessed, but none of these are what the above examples were talking about.
If we were to use a completely accurate metaphor, we would say in these cases that we are "Borrowing from Peter to pay Paul".
How important is this? Not very. As I said, everyone understands what the idiom represents, even if the language is not precise. However, I think it is an interesting mental exercise to challenge assumptions, including habitual use of words that may or may not be exactly correct.