The "Twist" in question:
So the twist is that the ISP has been given the responsibility for policing legitimate copyright violations, and there are monetary penalties for failing to do so.
Actually, that's not the twist. An ISP that gets a take-down notice, then it is generally protected if it takes down the material in question. I believe the person who put it up is entitled to some sort of notice and has the opportunity to show that it was not violating copyright (e.g., because the use was fair-use).
The "twist" was that BMG was attaching offers to settle to its take-down notices - which the ISP has to pass through to the person whose account is affected - as a way of getting the offender to pony up damages for each identified infringement.
Part of the problem in the case was that Cox was refusing to accept the take-down notices with settlement offers attached. However, that is not what led to the damages against Cox. What led to the damages was the conclusion that Cox was not implementing its take-down policy in a reasonable manner because, for example, it used "fake" account terminations where the account would be disabled, but would be reinstated upon request.
So, to be fair, this case didn't really change the landscape, it simply demonstrated that the requirements an ISP must satisfy to get the safe-harbor protection have some teeth - they actually have to make a good faith effort to implement their policy in a reasonable manner.
The problem here wasn't that BMG was putting a twist on the DMCA take-down notices, but that Cox was essentially thumbing its nose at its obligations under the DMCA while still claiming its protection.
