Remove nodes user does not have access to from list

Is there a way to modify the view pages and blocks created by the basic Workbench installation in order to display only the nodes that the current user viewing their Workbench has editing/viewing access to.

I have a test user named "workbench" and a user role named "workbench" where the user is to be greeted with a page upon login that only displays a certain content type in the list. The Workbench module gets me half-way there. It shows all the content, but only shows "edit" in the Actions column for content they can edit.

How do I remove the content which the "workbench" role does not have editing/modifying permissions for. I would like to be able to do this without actually specifying a role in the view. In my perfect website world, it would look at the current user's role, and display only content they have permissions to edit/delete/modify.

I would not like to specify which content types to list either, as that would defeat the purpose of drupal filtering the nodes based on the user automatically without specific declaration of either the role or the content type.

Here is a screenshot of what I mean. I would like "my room" to be removed because the user "workbench" cannot edit or delete that content type based on user permissions, whether they are the author or not will not matter. Other users will create nodes of the same content type. This "workbench" user will be a moderator for those types of content.

http://i.imgur.com/udnq7My.png