Platform: Windows
L&F: -Dswing.defaultlaf=com.sun.java.swing.plaf.windows.WindowsLookAndFeel
PASSES: JDK6 all, JDK7 b10
FAILS: JDK7 b20+
JCK tests, exist in JCK6 :
api/javax_swing/table/JTableHeader/AccessibleJTableHeader/index.html#AccessibleComponent[AccessibleJTableHeader0004]
api/javax_swing/table/JTableHeader/AccessibleJTableHeader/index.html#AccessibleContext[AccessibleJTableHeader0003] 

Please see the following code sample as a combined extract from the tests above:
--------------------------------------------------------------------------------
import javax.accessibility.*;
import javax.swing.*;
import javax.swing.table.*;
import java.awt.*;
import java.lang.reflect.InvocationTargetException;

public class Header {
    public static void main(String[] args) throws InvocationTargetException, InterruptedException {
        SwingUtilities.invokeAndWait(new Runnable() {
            public void run() {
                doTheTest();
            }
        });
    }

    private static void doTheTest() {
        JTableHeader header = new JTableHeader();
        AccessibleContext accessibleContext = header.getAccessibleContext();
        header.getColumnModel().addColumn(new TableColumn(0));
        try {
            //#AccessibleContext[AccessibleJTableHeader0003]
            System.out.println("trying getAccessibleChild(..)");
            accessibleContext.getAccessibleChild(0);
        } catch (Exception e) {
            e.printStackTrace();
        }
        AccessibleComponent accessibleComponent = accessibleContext.getAccessibleComponent();

        try {
            // #AccessibleComponent[AccessibleJTableHeader0004]
            System.out.println("trying getAccessibleAt(..)");
            accessibleComponent.getAccessibleAt(new Point());
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}
--------------------------------------------------------------------------------

When executed on JDK7b20+ with -Dswing.defaultlaf=com.sun.java.swing.plaf.windows.WindowsLookAndFeel


trying getAccessibleChild(..)
java.lang.NullPointerException
	at sun.swing.table.DefaultTableCellHeaderRenderer.getColumnSortOrder(DefaultTableCellHeaderRenderer.java:122)
	at com.sun.java.swing.plaf.windows.WindowsTableHeaderUI$XPDefaultRenderer.getTableCellRendererComponent(WindowsTableHeaderUI.java:126)
	at javax.swing.table.JTableHeader$AccessibleJTableHeader.getAccessibleChild(JTableHeader.java:860)
	at Header.doTheTest(Header.java:23)
	at Header.access$000(Header.java:7)
	at Header$1.run(Header.java:11)
	at java.awt.event.InvocationEvent.dispatch(InvocationEvent.java:217)
	at java.awt.EventQueue.dispatchEvent(EventQueue.java:603)
	at java.awt.EventDispatchThread.pumpOneEventForFilters(EventDispatchThread.java:276)
	at java.awt.EventDispatchThread.pumpEventsForFilter(EventDispatchThread.java:201)
	at java.awt.EventDispatchThread.pumpEventsForHierarchy(EventDispatchThread.java:191)
	at java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:186)
	at java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:178)
trying getAccessibleAt(..)
	at java.awt.EventDispatchThread.run(EventDispatchThread.java:139)
java.lang.NullPointerException
	at sun.swing.table.DefaultTableCellHeaderRenderer.getColumnSortOrder(DefaultTableCellHeaderRenderer.java:122)
	at com.sun.java.swing.plaf.windows.WindowsTableHeaderUI$XPDefaultRenderer.getTableCellRendererComponent(WindowsTableHeaderUI.java:126)
	at javax.swing.table.JTableHeader$AccessibleJTableHeader.getAccessibleAt(JTableHeader.java:818)
	at Header.doTheTest(Header.java:32)
	at Header.access$000(Header.java:7)
	at Header$1.run(Header.java:11)
	at java.awt.event.InvocationEvent.dispatch(InvocationEvent.java:217)
	at java.awt.EventQueue.dispatchEvent(EventQueue.java:603)
	at java.awt.EventDispatchThread.pumpOneEventForFilters(EventDispatchThread.java:276)
	at java.awt.EventDispatchThread.pumpEventsForFilter(EventDispatchThread.java:201)
	at java.awt.EventDispatchThread.pumpEventsForHierarchy(EventDispatchThread.java:191)
	at java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:186)
	at java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:178)
	at java.awt.EventDispatchThread.run(EventDispatchThread.java:139)