So what if they aren’t hosting the backend? How do you even define “the backend”? Is it the PHP frontend code serving the site? Or the database server?

Cloudflare definitely was hosting the content through their CDN. That’s hosting, there’s really no reasonable debate to be had about this.

The point is the site can come back online through an alternate CDN vendor, assuming they can find one that wants their business. The origin server(s) presumably are still online. The origin servers "host the site."

Sure, but the site can also come back online through an alternate hosting provider if their origin servers go down. How is that any different?

And even then, the concept of “origin server” is pretty vague.

"Origin server" is a well understood concept in CDNs.

My opinion is that if you're hosting controversial content, it's on you to provision redundancy. No company has the obligation to serve you if you piss them off, violate their TOS, whatever. So, yeah, you better be prepared with a back up host to switch to in a hurry.

If I have a group telephone discussion about how great the Nazi party was, is AT&T hosting the nazi discussion?

And if they ban me and I decide to use smoke signals to have this discussion is the sky hosting it?