Since Cotonti 0.0.2 you can (and should) set what user groups are allowed to download files associated with Pages.
In order to do that you should go to Administration => Users or Administration => Pages => Structure of pages (categories) and choose a Group or Category which you want to set permissions on. Click the permissions icon there.
After you have located permissions page, you need to switch to Advanced mode by clicking the More link a the bottom:
Then enable checkboxes in the third column (permission 1) on those categories/groups for which you want to allow downloads:
Click the "Update" button and then your Download permissions will be enabled.