Is it possible to use an external Identity Provider in a Web API with ASP.NET 5?

Reading this question, @Pinpoint’s answer and the further discussion on comments, I’m well aware that natively we can’t add an identity provider to our apps developed with ASP.NET 5. One possible replacement for the legacy OAuthAuthorizationServerMiddleware is then provided by the AspNet.Security.OpenIdConnect.Server as I’ve found in many places.

Why call SignOut(DefaultAuthenticationTypes.ExternalCookie) before use of ApplicationCookie with ASP.Net Identity?

Why does this example call the SignOut for ExternalCookie before signing in with an ApplicationCookie? Is it just a way to make sure the authentication information is clean? (The full example is here: http://www.asp.net/identity/overview/getting-started/introduction-to-aspnet-identity)

Using ASP.Net Identity 2 cookie in forms authentication

I have an Owin Identity application and another application set up in a virtual directory. The virtual app is set up using traditional forms authentication, and both Web.configs have the same <machineKey> set. I can login using the Identity app, and can see the resulting cookie. However, when I try to access the virtual app it says I am not authenticated.