GridPane layout affected by Accordion (SSCCE provided)

(Full description with images on http://stackoverflow.com/questions/16472589/layout-gridpanel-borderpanel-button-accordion)
Here is two snapshots of a SSCCE written to show a strange behavior of layout with or without accordion as a cell into a GridPane, the code to reproduce these behaviors and finally the questions I ask.

Good rendering, as expected, the "center" content of the BorderPane is a Label:
![Bad layout of the button][1]
http://i.stack.imgur.com/rtox4.png

Bad layout of the button, the "center" content of the BorderPane is an Accordion:

![Bad layout of the button][2]
http://i.stack.imgur.com/WxsXo.png

The code:

    import javafx.application.Application;
    import javafx.geometry.HPos;
    import javafx.scene.Scene;
    import javafx.scene.control.Accordion;
    import javafx.scene.control.Button;
    import javafx.scene.control.Label;
    import javafx.scene.control.TextField;
    import javafx.scene.control.TitledPane;
    import javafx.scene.layout.BorderPane;
    import javafx.scene.layout.GridPane;
    import javafx.scene.layout.Priority;
    import javafx.stage.Stage;
    
    public class SSCCE extends Application {
    
       public static final boolean TOO_BIG_BUTTON = true;
    // public static final boolean TOO_BIG_BUTTON = false;
    
       public static void main( String[] args ) {
          launch( args );
       }
    
       @SuppressWarnings("nls")
       @Override
       public void start( Stage stage ) {
          TextField tf = new TextField( "textfield" );
          BorderPane bp = new BorderPane();
          Label lv = new Label( "BorderPane - Center - Center - Center - Center - Center" );
          lv.setPrefHeight( 96.0 );
          if( TOO_BIG_BUTTON ) {
             Accordion acc = new Accordion();
             TitledPane tp = new TitledPane( "Titled pane", lv );
             acc.getPanes().add( tp );
             acc.setExpandedPane( tp );
             stage.setTitle( "SSCCE - too large button" );
             bp.setCenter( acc );
          }
          else {
             stage.setTitle( "SSCCE - as expected" );
             bp.setCenter( lv );
          }
          GridPane gp = new GridPane();
          Label lbl = new Label( "Label: " );
          Button btn = new Button( "button" );
          btn.setMaxWidth( Double.MAX_VALUE );
          gp.add( lbl, 0, 1 );
          gp.add( tf , 1, 1 );
          gp.add( btn, 2, 1 );
          gp.add( bp , 0, 2, 3, 1 );
          GridPane.setHgrow( tf , Priority.ALWAYS );
          GridPane.setHgrow( btn, Priority.NEVER );
          GridPane.setHalignment( btn, HPos.RIGHT );
          stage.setScene( new Scene( gp ));
          stage.centerOnScreen();
          stage.show();
       }
    }

The questions:

- Why?
- How can I help the layout manager to compute the right size of the button?

  [1]: http://i.stack.imgur.com/rtox4.png
  [2]: http://i.stack.imgur.com/WxsXo.png