Anonymous customers cannot purchase downloads

So, isn't this an issue with Commerce File then?

(my apologies if I'm mistaken)

I was under the impression that completing a checkout automatically creates a drual user for the visitor. He should be able to login and get the file.

I switched this back to a feature request. One of the developpers will have to take a look.

If the file is free of charge, a user isn't created. My use case follows the donation model, where the user adds the product to the card and has the option to donate some amount to the artist, but the donation is optional. If the donation is optional and the price is $0.00, there's no need to collect billing information. The user should be able to finish the checkout and get the file.

Commerce File does not support anonymous access to purchased files. After order completion, it creates an access license that links the file to the user id.
Perhaps #1412252: Direct file download link could provide a solution for a one time access.

I have just published 7.x-2.x which supports this:
https://drupal.org/node/1395488#comment-7658191

Tagging for possible backport if a 7.x-1.x maintainer steps up.