For my own part, I would question that there is a non-ephemeral identification of participants, namely by requiring the inputs first. The inputs would serve as an identification and if any problems were subsequently to arise, they could be blacklisted.
But if the inputs are really not connectable to the outputs could I jam the transaction by using outputs that add up to greater than my inputs?
In this case could anyone work out that it was me that put in the outputs that made the transaction not balance?