How do I get Static Site (just a index.html) S3 object properly CNAME'd through Cloudflare?

I have a bucket and in that bucket is a style.css and index.html

all I want to do is use Linode's s3 to serve up that index.html through the use of a CNAME. But it will not return index.html if you run it through cloudflare. If you run it through non-cloudflare (for instance, I'm using another domain with name.com CNAME) and it drops the TLS/SSL support that the docs say that its supposed to have.

My bucket name and subdomain do -NOT- match and I don't want them to match. I can make them match if required but I really don't want to add the extra characters if I don't have to.

I'm referencing this: https://www.linode.com/community/questions/19557/object-storage-static-site-not-serving-indexhtml-when-accessed-via-external-doma

There's another post in there that basically says, from the Linode staff "This is broken and the solution is to use our own DNS servers".

I just want to know: Is this still the answer? Because if this is still the answer then I'm moving my S3 storage elsewhere. It should not be this hard to host a single index.html file that's 2kb big.