Enabling POST/PUT/DELETE on AWS CloudFront?

In AWS CloudFront I set this within: "Allowed HTTP Methods" in the "Default Cache Behavior Settings" area: GET, HEAD, OPTIONS, PUT, POST, PATCH, DELETE

Then in AWS S3 I set CORS configuration to:

<?xml version="1.0" encoding="UTF-8"?>
<CORSConfiguration xmlns="http://ift.tt/1f8lKAh">
    <CORSRule>
        <AllowedOrigin>*</AllowedOrigin>
        <AllowedMethod>GET</AllowedMethod>
        <AllowedMethod>PUT</AllowedMethod>
        <AllowedMethod>POST</AllowedMethod>
        <AllowedMethod>DELETE</AllowedMethod>
        <AllowedMethod>HEAD</AllowedMethod>
        <MaxAgeSeconds>3000</MaxAgeSeconds>
        <AllowedHeader>Authorization</AllowedHeader>
    </CORSRule>
</CORSConfiguration>

However when I run it through curl I get:

$ curl -I -s -X POST -H "Origin: www.example.com" [hash_here].cloudfront.net
HTTP/1.1 405 Method Not Allowed
Content-Type: application/xml
Transfer-Encoding: chunked
Connection: keep-alive
Access-Control-Allow-Origin: *
Access-Control-Allow-Methods: GET, PUT, POST, DELETE, HEAD
Access-Control-Max-Age: 3000
Vary: Origin, Access-Control-Request-Headers, Access-Control-Request-Method
Allow: GET, DELETE, HEAD, PUT
Date: Sun, 01 Mar 2015 14:12:26 GMT
Server: AmazonS3
X-Cache: Error from cloudfront
Via: 1.1 5896eef8502a96757950c7d389f2015c.cloudfront.net (CloudFront)
X-Amz-Cf-Id: uBK_gStEvSTWypvU8_YYjtfjC2UzdR3Ff_cDLitMaeUBNZ9AgrSkJg==