The remove friend option works from your end, but what I have found is that I must still be on the other persons list as they have not removed me.
I found this out by a few people I have removed from my end inviting me to play, showing that I am still on their list of friends.
Mes.
PS: doesn't bug me as I remove people periodically because I have not seen them or what have you just throwing the info out there as in theory when you remove a friend you would think you are automatically removed on the other end.