Page.User.Identity.IsAuthenticated gets its value from Page.User (obviously) which is unfortunately read-only and is not updated when you call FormsAuthentication.SignOut().
Luckily Page.User pulls its value from Context.User which can be modified:
// HttpContext.Current.User.Identity.IsAuthenticated == true;
FormsAuthentication.SignOut();
HttpContext.Current.User =
new GenericPrincipal(new GenericIdentity(string.Empty), null);
// now HttpContext.Current.User.Identity.IsAuthenticated == false
// and Page.User.Identity.IsAuthenticated == false
This is useful when you sign out the current user and wish to respond with the actual page without doing a redirect. You can check IsAuthenticated where you need it within the same page request.