The close action wasn't necessary at all.
Here is a working jsFiddle where I kept only the necessary parts and added willDestroyElement to the component: http://jsfiddle.net/NQKvy/421/
App.ModalDialogComponent = Ember.Component.extend({
didInsertElement: function () {
var self = this;
this.$('.modal').modal('show');
this.$('.modal').on("hidden", function () {
self.sendAction();
});
}
});