Is it not possible to use public access and have umbracoUseDirectoryUrls set to true at the same time?

When call the page /secure.aspx it's working as it shoud, but when calling the page without aspx like /secure I get this exception

Object reference not set to an instance of an object.
   at System.Web.Security.Membership.GetCurrentUserName()
   at System.Web.Security.Membership.GetUser()
   at umbraco.requestHandler..ctor(XmlDocument _umbracoContent, String url)
   at umbraco.UmbracoDefault.Page_PreInit(Object sender, EventArgs e)
   at System.Web.Util.CalliHelper.EventArgFunctionCaller(IntPtr fp, Object o, Object t, EventArgs e)
   at System.Web.Util.CalliEventHandlerDelegateProxy.Callback(Object sender, EventArgs e)
   at System.EventHandler.Invoke(Object sender, EventArgs e)
   at System.Web.UI.Page.OnPreInit(EventArgs e)
   at System.Web.UI.Page.PerformPreInit()
   at System.Web.UI.Page.ProcessRequestMain(Boolean includeStagesBeforeAsyncPoint, Boolean includeStagesAfterAsyncPoint)

I have protected the page via role based protection.