How to select all text in JTable cell when editing

I would like to have the editor in my editable JTables select all text in the cell when starting to edit. I have tried a couple of things that all revolve around calling JTextComponent.selectAll() on the component that is returned from the TableCellEditor.getTableCellEditorComponent method. None of the things I tried worked.

In my latest attempt, I altered the SimpleTableDemo class from the Swing tutorial to use a custom TableCellEditor that calls the selectAll method. In the debugger I can see that the selectAll() method is being called, but the table still goes into edit mode without selecting the text in the cell (or perhaps the selection is being cleared before display). That code is below. Can anybody tell me where I'm going wrong?

import javax.swing.DefaultCellEditor;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.JScrollPane;
import javax.swing.JTable;
import javax.swing.JTextField;
import javax.swing.JTree;
import javax.swing.table.TableColumn;
import javax.swing.table.TableColumnModel;
import javax.swing.text.JTextComponent;


import java.awt.Component;
import java.awt.Dimension;
import java.awt.GridLayout;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;


public class SimpleTableDemo extends JPanel {
    private boolean DEBUG = false;


    public SimpleTableDemo() {
        super(new GridLayout(1, 0));

        String[] columnNames = {"First Name",
                                "Last Name",
                                "Sport",
                                "# of Years",
                                "Vegetarian"};

        Object[][] data = {
                {"Kathy", "Smith", "Snowboarding", new Integer(5), new Boolean(false)},
                {"John", "Doe", "Rowing", new Integer(3), new Boolean(true)},
                {"Sue", "Black", "Knitting", new Integer(2), new Boolean(false)},
                {"Jane", "White", "Speed reading", new Integer(20), new Boolean(tr