What about just being honest and not looking for loopholes to keep something that doesn't belong to you?
I call bullshit. If you keep something knowing it is not yours you are anything but blameless. In New York it is actually a crime.
In fact, they might be testing your honesty by doing it on purpose and it looks like you're failing so far.
I know someone who kept the money from a banking error. She is now blacklisted from having a bank account in the US. Not fun.
An integral part of each agency's payroll responsibility is to detect, correct and recoup overpayments made to employees.
A person acquires lost property when he exercises control over property of another which he knows to have been lost or mislaid, or to have been delivered under a mistake as to the identity of the recipient or the nature or amount of the property, without taking reasonable measures to return such property to the owner. [emphasis mine]