[dfee]

No. You’re not providing your Facebook cookie to the third party site. So, there is no way to associate your identity on example.com with your Facebook profile.

Think of it this way, if you have an authentication ticket, such as what is in a session cookie, then you have access to your account. If someone intercepted that ticket / cookie, they could maliciously act on your behalf and play around on your Facebook - just like you. Your browser therefore doesn’t send cookies to domains that aren’t specified as trusted by the originator of the cookie; I.e. third parties.

So example.com and Facebook wouldn’t be able to associate the two identities.

*except of course through some interesting trickery like browser fingerprinting.