Thanks to everyone for the comments. As of today the matter is now closed. A new letter is being sent out indicating that everything is fine and the $6000 bill has gone away.
It was indeed them not having checked the supporting documents prior to sending out the letter.
However I still find it odd that I needed to send them a SIN (issued by govt), passport (issued by govt) and other supporting docs (some issued by the govt) to prove to the govt that the children exist
