Does any restriction exists in FQL if I need to read a post from stream table, where PostID is some arbitrary id of non-friend's public post?
In other words, does reading from stream table currently only means I am allowed to read posts that I am friend/follower of?
No, that's not the case, but you'll need a User Access Token with read_stream permissions according to https://developers.facebook.com/docs/reference/fql/stream/#permissions even if you want o access public posts.
Be aware that with v2.0 of the Graph API https://developers.facebook.com/docs/facebook-login/permissions/v2.0#reference-extended-read the read_stream permission is reserved for apps that replicate the Facebook client on platforms that don’t have a native client.
