just saying.... while in practice all of us when there is no other choice but to self-refer, we do get both the referral bonus and sign-up bonus, but I will not say there is "no reason" if it doesn't work. Technically self-referral is against the T&C, and hence that is the most obvious reason for it to not to work. AMEX could always do a full audit and reverse all these bonus if they really want to.
Chasing AMEX for the Sign-Up Bonus is rather easy, but if you don't get the referral bonus automatically, it will be a bit more difficult (not say it can't be done) if you need to provide the "friend" that you referred... like, it will be rather hard for you to say "I refer alc, he is my friend, just happen to have the same full name, d.o.b. and address as me. please add the referral bonus for me, thank you"
Self-referral has worked every single time I have done it for regular AMEX and Aeroplan AMEX. I don't think AMEX really care enough about who you are referring... I am not sure where in the terms and conditions it says you cannot refer yourself either...I thought it just said you have to know the people you are referring.