We all know about hacks, scams, password leaks and all the shit that's happening in the crypto world and we also see lots of scammers using mixers to eradicate the possibility of them being caught at all (though there are traces, but using mixer saves these scammers at the least, not intentionally).
Now, let's say that a hack happened some day at some exchange for about $300 million (or even $3 million, just e.g.), and the exchange immediately opens up about the hack. For a second, just think that the scammer keeps the coins in his wallet and doesn't move them for some time, however FBI and other major authorities are aware of this hack and they give orders to mixers that if a specific address is provided to the mixers (if they know exactly on which address the hacker has kept the coins), and they ask them to immediately report them about the same, then let me ask some questions:
1. Do mixers know where they're getting a deposit from?
2. If yes, will they co-operate here with the officials and let them know about the deposit?
3. If they do, how will they stop the scammer from moving his funds out of their mixer?
Generally hackers will try to cash out the stolen funds as soon as possible because they know that more longer they keep then it eill be harder for them to convert.
But as you said if there is such situation then the mixer has to manually blacklist any transactions coming from the listed address so they won't get into any trouble.
They're not really supposed to answerable to authorities but if they do when they feel that is the right thing then it can change the face of mixers from only funds mixed here are coming from illicit activities to they're here to give better privacy to individual and not to help the scammers.