This is literally the business model. The owner of an IP address is responsible for the content delivered from that IP address. Cloudflare would like to have it both ways -- they get to multiplex sites behind their network infrastructure and accept money for the service, but not be responsible for the content that they deliver, because it originally came from somewhere else.
In case the use of "literally" wasn't enough of a clue, this is incorrect. For the same reason that the DNS service, the ISP, or the internet itself are not responsible for the content.
