place caret at the beginning of static keyword - the lightbulb appears. Click alt-enter - "There are no items to show in this menu" tooltip appears.
1. There should be no lightbulb
2. It's rather complicated to remove the tooltip.

PS Note, the code is changed in 4.0.1

    static EditorParameterInfoHandler()
    {
      ourPopupChars = new OneToListMap<PsiLanguageType, char>();
      
      ourContextFactory = new List<IParameterInfoContextFactory>();
      foreach (IParameterInfoContextFactory contextFactory in ParameterInfoPopupControllerImpl.Instance.ContextFactories)
      {
        AddContextFactory(contextFactory);
      }
    }

Issue was closed