By design, the built-in Preview dialog of RadFileExplorer works with images and text files(txt) for all other file types a download dialog is prompted - thus if the item in the library is an image or text file it will be displayed in the Preview Dialog.
Regarding the permissions, the SPContentProvider from the following blog post is taking into account user's permissions when displaying libraries. If you are not using this provider I would strongly recommend to switch to it.
Using the RadFileExplorer for ASP.NET AJAX in SharePoint 2010 web parts
the Telerik team
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