When an anonymous user is creating a ticket and tries to attach a file to it, it gets the following error message:
Cannot attach file: Unknown server error (404).

The network response message is the following:
No project could be found with id '10103'.

This happens because in the project permissions, although the group 'Anyone' has permissions to 'Create Issues' and 'Add Attachments', it does not have permissions to 'Browse Projects'.

Unless there is a workaround, it seems that this functionality to add attachments anonymously is missing.