How do I log out from Facebook when using OAuth server-side? - asp.net-mvc

Question

I'm using OWIN with ASP.Net Identity to enable users to log in to a site using their social media credentials.
As part of this we also request extra permissions for interacting with their account.
This is working fine for Twitter and Facebook for the most part, except when trying to log out from the site when using Facebook for the log in.
If you log out of the ASP.Net app you are still logged in to Facebook. That's not a problem in itself, but when you return to the ASP.Net app you're automatically logged in using the Facebook account you used before and you're given no chance to choose a different account.
As the user you can navigate to Facebook, log out, then return to the ASP.Net app and you'll get asked to log in again, but that's not a very nice process for the user to go through. Simply explaining that to a user will be messy and there's plenty for them to get wrong (logging out in a different browser, not reading the help text, etc).
An answer on this question suggests using the javascript SDK which isn't too awful to implement: Logging out from facebook when using MVC 5 OWIN
Some of the answers say "that's how it's supposed to work", but we expect our users to be using multiple accounts with this application so a reasonable log out process is required. Also Facebook themselves say we should log people out of Facebook when logging out of our application: https://developers.facebook.com/docs/facebook-login/web#logout
Note: This function call will also log the person out of Facebook. The reason for this is that someone may have logged into your app and into Facebook during the login flow. If this is the case, they might not expect to still be logged into Facebook when they log out of your app. To avoid confusing people and to protect personal security, we enforce this logout behavior.
But that bring me to the current issue I'm encountering.
I have the following Typescript/Javascript code which performs the log out:
FB.getLoginStatus((getLoginStatusResponse) => {
if (getLoginStatusResponse.status === 'connected') {
FB.logout((logoutResponse) => {
$("form[id='logoutForm']").submit();
});
} else {
$("form[id='logoutForm']").submit();
}
});
getLoginStatus returns fine saying that the user is logged in (status === 'connected') === true.
But then, when I make the logout call I can see the API returns a 302 Not Found, and the redirect points to the facebook home page.
The Facebook Javascript SDK handles this by swallowing the error and not calling the logout callback.
Why am I getting a 302 for an official API call made when I have confirmed the user is logged in?
And is there another way to achieve the log out? A server-side solution would be perfect! Although I don't want to use anything that's undocumented/unsanctioned.