Facebook provides apis for http requests to interact with their system. However for some apis, you much authenticate the user by Oauth. Oauth requires a web browser, there is no web browser on the YCTV, so much of the facebook api cannot be used from the YCTV platform. Facebook's rules are "Unless you are writing a browser, or are employed by facebook, you may not request a user name and password from the user." Please check the facebook website for information about their APIs.
I think this response maze overlook a best practice. Note that you can use your own servers or facebook apps to provide authorization.
For example, i have an eye-fi sd card in my camera that uploads photos directly to facebook using wifi. This works because I log in to an eye-fi app server ahead of time and authorize the eye-fi app to do these things, and then my card communicates with the eye-fi app server.
Similarly you can write your own site or facebook app where the users login to facebook with oauth. Your tv app can then relay communication through your own site / app that the user has logged into and authorized. This may be complex for a widget developer, but should not be a big deal to a web service developer.