Sharing scope between controller & directive in AngularJS

I've created a directive to wrap a jQuery plugin, and I pass a config object for the plugin from the controller to the directive. (works)

In the config object is a callback that I want to call on an event. (works)

In the callback, I want to modify a property on the controller's $scope, which does not work. Angular does not recognize that the property has changed for some reason, which leads me to believe that the $scope in the callback is different than the controller's $scope. My problem is I just don't why.

Can anybody point me in the right direction?

Click here for Fiddle

app.js

var app = angular.module('app', [])
    .directive('datepicker', function () {
        return {
            restrict: 'A',
            link: function (scope, element, attrs) {
                // Uncommenting the line below causes
                // the "date changed!" text to appear,
                // as I expect it would.
                // scope.dateChanged = true;

                var dateInput = angular.element('.datepicker')

                dateInput.datepicker(scope.datepickerOpts);

                // The datepicker fires a changeDate event
                // when a date is chosen. I want to execute the
                // callback defined in a controller.
                // ---
                // PROBLEM: 
                // Angular does not recognize that $scope.dateChanged
                // is changed in the callback. The view does not update.
                dateInput.bind('changeDate', scope.onDateChange);
            }
        };
    });

var myModule = angular.module('myModule', ['app'])
    .controller('MyCtrl', ['$scope', function ($scope) {
        $scope.dateChanged = false;

        $scope.datepickerOpts = {
            autoclose: true,
            format: 'mm-dd-yyyy'
        };

        $scope.onDateChang