We have a simple task recently and that was to enable anonymous access in a site. So easy right? but sometimes it happens if you are not aware how it works, it takes lot of time. Here is same scenario. As we have set up anonymous access, client uploaded some files in library and put it links on a public page. It works fine if you have edit/ full control for site. But if you are anonymous user, you are asked to login.
As I said earlier, if you know how it works, you will be able to solve it easily. Only you need to make sure that items are published with major version. If that is done, anonymous user will be able to download files without any issue.
If you search google, you will find that you need to provide "Open item" access to items. If above solution do not solve the issue, below are links to set up open access:
en-ph/help/2498047/anonymous- users-cannot-open-xlsx-files- from-a-sharepoint-document- libr
microsoft.com/acasilla/2011/ 10/01/add-openitems- permission-to-the-default- anonymouspermmask64-enabling- opening-of-office-docs-within- an-anonymous-accessible- sharepoint-site/
wordpress.com/2012/05/29/how- to-make-list-items-visible-to- anonymous-users-in-search/