Imagine you are a cashier and you have a drawer with ten $100 bills.
A customer comes in and says, "Here's $100 can I exchange that for your $100"
You look at his bill, it looks the same as your bill. So you give him $100 and put his bill on the bottom of your pile of $100.
This happens all day until all of your original $100 bills are gone, and have been replaced with the identical $100 bills.
You leave work with the handful of $100 bills, and you go to the bank. You try to deposit the bills, but the bank says, "Sorry, these aren't real."
That's what Mt Gox has, basically... A stack of worthless bitcoins that were already spent.
So they never checked if they had the correct private keys!?