If this is HTTPS, how would Cloudfare have the certificate for your domain so that browsers don't warn about a mismatch?
Or is it that when you sign over DNS to a provider, they can take over your cert? They can "ass-cert" their own? :)
As far as I know they terminate all TLS; it’s one of the tradeoffs using them.
Yes, the person who controls the DNS controls the certificate.
What a certificate is supposed to verify is that traffic is going to the right place. If you designate cloudflare as the rightful host of your website then they can get a certificate.
This isn't an edge case though. This is cloudflare's primary product. It is why users use them.