When a Facebook connected app or site has access to "your profile" that includes your friends list.
Anyway as I can see that you failed to read for comprehension I must reiterate that allowing next-door to read your Facebook profile in no way authenticates you to the site, nor does it provide them with your profile picture.
Slight correction - it has access to your friends who have also used the facebook login for that site.
If you're the first person to login, the site will get an empty list. Only the set of your friends who have previously used the service, will show up if the service queries fb for your friends.
Anyway as I can see that you failed to read for comprehension I must reiterate that allowing next-door to read your Facebook profile in no way authenticates you to the site, nor does it provide them with your profile picture.