DMCA safe harbour
In the US Cloudflare should be in the clear by claiming Safe Harbour, which was designed for something else but should easily cover this. The only aspect they're vulnerable on is failing to act on a cease and desist case if they've been instructed not to provide services for insert-name-here, but that would be contempt anyway.
DMCA was almost specifically designed to protect US copyright without penalising US video service providers, like YouTube. Non-US copyright holders have much reduced rights and non-US service providers find it harder to claim Safe Harbour. This is standard US trade policy via extra-territorial enforcement.
Biting the hand that feeds IT
