Cloudflare: - Makes a website available through their IP addresses - Resolves a site's DNS - Stores the content of the website on their servers, to serve to clients. The fact that there's an expiration on that content is of no consequence.
The fact that the final source-of-truth lies offsite makes no difference. If I rent a regular, run of the mill server and have it proxy all requests to a different server, does that suddenly make the first host bulletproof to any and all scrutiny?
Cloudflare likes to pretend they are a neutral entity, impartial, just like regular Internet Providers but they are decidedly not. They are being paid by their customers to store and serve their content from their servers and to perform traffic filtering.
If CloudFlare provided a way to find out the host of a website they run, and gave said host a way to find out what servers specifically are hosting it, they'd have a much better argument, because they'd make it easy for anyone to use the legal system to go after offenders.
I don't know how easy it is for US citizens or law enforcement to get that information from CF, but from what I've heard, it's very, very hard to do so from Europe, and will basically only be used for major crimes, but not for a common "scam a granny" operation. CF is essentially providing cover for these.
Surely they respond to subpoenas and warrants.
For all intents and purposes, that means they don't for anyone outside the US, except for very high profile cases. For everything else, they're providing a legal shield.