Currently, in my main page, I'm displaying a brief list of documents added to the site recently.
Now, not every user is allowed to see the contents of every document library, so I wonder if this rule applies to my recent documents Data View without any modification from me.
So that, if I'm not allowed to see the contents of document library A, I shouldn't be able to see any documents from A, in the Recent Documents.
Data view web parts respect item level permissions. If none were set, then all users who has access to the library will see them until permissions are changed. Items with item level permissions will only show up if the user has the rights to see it.
sharepoint search basically comes in the following 4 flavours:
all of them respect ALL ACL's (Access Control Lists) available, down to listitems (or, if your crawling say a filesystem, file security).
Any search will retrieve all documents fitting the query, which sharepoint will then "trim": i.e remove all items the user has no access to.
