If you and someone else both send money to Wikileaks, you both sign your transactions. The transactions, even for identical amounts, are not identical. For one thing they will name different unspent txouts to spend; for another they'll have different timestamps. For a third thing they will specify different addresses for "change" to come back to. All of these things will be combined in a hash function to give your transaction a transaction ID which is unique.
There is no way in a transaction to determine what is "my output" and "your output". That is what makes coin join work, but also brings up the problem originally posed.