You sure about that? I just uploaded a file and then..

    curl -o /dev/null -v https://nofile.io/f/01ZAJO7Qhfe

    *   Trying 104.18.59.89...
    * Connected to nofile.io (104.18.59.89) port 443 (#0) 
    * TLS 1.2 connection using TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256
    * Server certificate: sni212289.cloudflaressl.com
    * Server certificate: COMODO ECC Domain Validation Secure Server CA 2
    * Server certificate: COMODO ECC Certification Authority
    * Server certificate: AddTrust External CA Root
    > GET /f/01ZAJO7Qhfe HTTP/1.1
    > Host: nofile.io
    > User-Agent: curl/7.43.0
    > Accept: */*
    >
    < HTTP/1.1 200 OK
    < Date: Tue, 07 Mar 2017 15:18:16 GMT
    < Content-Type: text/html; charset=UTF-8
    < Transfer-Encoding: chunked
    < Connection: keep-alive
    < Set-Cookie: __cfduid=d3f6984a870cdd03cea954585ac19e38c1488899895; expires=Wed, 07-Mar-18 15:18:15 GMT; path=/; domain=.nofile.io; HttpOnly
    < Vary: Accept-Encoding
    < Strict-Transport-Security: max-age=15768000
    < Server: cloudflare-nginx
    <
    { [957 bytes data]
    * Connection #0 to host nofile.io left intact

Looks like that ran through Cloudflare, even if it wasn't cached. Doesn't look like it's going directly to whatever storage you are using.