Event.stopPropagation() not working for KeyDownEvent

I have a user login form that I want submitted if the user presses ENTER in the password field or clicks the login button. So I add a KeyDownHandler:

KeyDownHandler kdh = new KeyDownHandler() {
  @Override
  public void onKeyDown(KeyDownEvent event) {
    if (event.getNativeKeyCode() == KeyCodes.KEY_ENTER) {
      event.stopPropagation();
      login_btn.click();
    }
  }
};
password.addKeyDownHandler(kdh); 

The login button calls the presenter to doLogin(). Before sending the request to the server, the method checks that the fields are filled in. If not, an alert is popped up.

I want this alert to hide on ENTER or ESC, so the alert has a method:

@Override
public void onPreviewNativeEvent(Event.NativePreviewEvent event) {
  Event nativeEvent = Event.as(event.getNativeEvent());
  int c = nativeEvent.getKeyCode();
  if (c==KeyCodes.KEY_ENTER || c==KeyCodes.KEY_ESCAPE) {
    hide();
  }

}

Problem: The alert pops up and disappears all on a single ENTER.

Why isn't Event.stopPropagation() stopping the ENTER key? Why should I even need to try since the alert is only created when the error is detected? How can I accomplish this (other than Window.alert())?

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