They do not. Archive.is gives back the IP for Cloudflare if the DNS request comes from Cloudflare. There are previous discussions here I dont have the link handy about how the admin of Archive.is does not like that Cloudflare does not forward EDNS Client Subnet information so they give CF their own IP. This causes the client to go to CF despite Archive.is not being a customer of them.

It's the effect of Archive.is banning Cloudflare for not giving up Client Subnet information. The end result is being directed to CF despite Archive.is not being behind them and thus one getting into captcha loops.