This is an interesting BBC interview where a woman was scammed into using Western Union and Money Gram to transfer into someone elses account. While the money transfer systems are safe when treated with care, people need to remember that their account information is as important as their bank account login and passwords and should be kept very secure.
So, the moral of the story is never give out your information to a third party. There are plenty of ways to get the money to another person without ever giving them your account details.