How can "undo" bitcoin transactions be "private"? BitUndo private transactions:


  If you choose to make your undo transaction private, nobody will be
  able to see that you tried to undo a transaction, unless it succeed.
  You have to know that a private undo transaction has less chances to
  succeed, as is not distributed in the whole bitcoin network.


From what I know, for a undo transaction to even stand a chance of competing with the main transaction, it has to be broadcasted to the public network.

If so, then how does Bitundo "private transactions" work?
The failed transaction won't get stored in a block on the blockchain, so it will be hard for an average person to find them.  I think most of the Bitcoin nodes will delete them from memory eventually.

Also, these sneaky undo transactions are probably not broadcast so publicly in the same way that normal transactions are; they are probably sent to a smaller network of miners who want to participate in this undo system.