Unless the owners of these sites can show the authorities that they are taking precautions to prevent the flow of such dirty coins to the mixers, they will be considered as illegal by the government.
If the owners are willing to provide the logs then what is the use of advertising as bitcoin mixers, either they must advertise that they will be showing the logs if the authorities will approach them through a legal process and if that disclaimer is crystal clear for the clients who use their service then they can provide those details and everyone can use their service according to their terms. The problem with that is some government might target bitcoin traders because of ban in their country and if they produce court documents then you cannot release those sensitive information to those government and where do you draw the line is the question,