At least, I think, it is incorrect, because javadoc is not too rich, to think anything else.

So, code:

    @Override
    public void start(Stage primaryStage) {
        final ToggleGroup tg = new ToggleGroup();

        ToggleButton tb1 = new ToggleButton("toggle 1");
        final ToggleButton tb2 = new ToggleButton("toggle 2");

        tg.getToggles().addAll(tb1, tb2);

        Button b = new Button("Select toggle");
        b.setOnAction(new EventHandler<ActionEvent>() {
            @Override
            public void handle(ActionEvent t) {
                tg.selectToggle(tb2);
            }
        });

        primaryStage.setScene(new Scene(new VBox(tb1, tb2, b)));

        primaryStage.show();
    }

We have 2 toggle buttons, and 1 button. That button selects "toggle 2" in the toggle group.

To reproduce:
1) click button -> toggle 2 is selected. ok
2) click button -> toggle 2 is unselected. <- that is strange, because I ask to select it (javadoc is incorrect?)
3) click button * n times (n > 0) -> nothing happens (toggle 2 is not selected any more).

Issue came from : http://stackoverflow.com/questions/14885346/togglegroup-selecttoggle-bug