Facebook friends list

Right this one’s baffled me a little. I have a friend who I am friends with and their friends list is set to public, they have told me that they are no longer friends with somebody but when I go onto my friends profile the apparently unfriended friend is still showing up as the first picture in their top 6 on profile page but when you actually go through his friends list the person isn’t in his list so are they still friends or not?