I spoke with one of the developers about this this, and apparently it is possible to do, but not directly.
From the Attribute Viewer, you can get a list of Tabs. Each Tab has TabContent which you can get from controls. You loop through controls to get the content and can then pull a GridView and/or a DataSource (a .NET datatable), if you prefer to grab that.
A small piece of sample code might look something like this:
foreach (TabPanel tab in viewer.Tabs)
TabContent content = tab.Controls as TabContent;
DataTable tabInfo = content.DataSource;
GridView grid = content.GridView;