The last time I checked a CD it also contained similar wording regarding Unauthorised Commercial Use and public preformance Prohibited, so if you take the words "public performance" and "commercial use" to the letter of the law as some are doing above, then we are all breaking the law as soon as we play a CD to an audience. Like downloads, CD's are sold to the public on a non commercial basis. A bit like hiring a DVD from Blockbuster, you can hire one and show it at home, but not in a hospital, prison, nursing home etc - that would be illegal.
If you are using CD music in order to make money at a private function which is by definition, not covered by PPL licence requirements this would make it an unauthorised commercial use, because it is not licenseable.
Using CD's at a private function may not be penalised under the Public Performance section of the copyright prohibition, but it could be enforced under the Commercial Use area, since you are charging a fee, and the only way to meet both criteria would be to do private functions and work for nothing.
So it seems to me that we have one common denominator here, whether it's CD's or legal downloads, in that they both carry the same limited use.
Do you also know that the onus is on us, to check that the venue (or function room in the case of private functions) has a current, valid entertainment licence?, but how many of us actively ask to see and check this document?. If you are working a public function in a pub and the venue hasn't renewed it's entertainment licence or there are restrictions, then the DJ needs to obtain a PPL licence for the night, if not we are breaking the law, regardless.
Many venues do take liberties, especially over Xmas and how many unlicensed venues will be taking the risk this Saturday?
Oh and by the way, under some ancient law, it's also illegal to dance on the sabbath day, so remember to tell your audience that after 12.00 on New Years Eve otherwise you may find yourself clapped in irons in the Tower of London.