How to import XML (using an API) via Feeds module?
You need todo more debugging. As 1 possible debugging example use Chrome Inspector to assure that properly configured, Feeds is requesting the correct URL to get the XML payload. you can do this by logging HTTP persistently before you hit the drupal admin page and recording what Feeds is issuing.

Compare that to hitting the URL by hand in the browser, or whatever steps you take. I suspect that Feeds has an API to alter the outbound request to the remote server and make it 1:1 with hitting the remote url by hand.

There are other HTTP session records you can use depending on your OS.