Wrong! I have heard this "urban myth" at least a million times (at least it seems like a million), and it is nonsense. If you are in violation of your contractual agreement with your creditor, they can sue for the entire balance of the debt.
Of course you have a moral obligation as well as a legal obligation to pay your just debts, and I don't want to discourage you from paying what you can afford to pay, if you are not able to pay the full amount of what you owe.
But it won't necessarily keep you from being sued, and a creditor would be within their legal rights to do so.
And not only that, but if the contractual agreement or state law provides for it, the creditor can also seek recovery of their attorney fees and costs, in addition to the amount of the debt.