Public key crypto provides a global concept of identity: Choose a key pair and distribute the public key and no one else can claim your identity so long as you conceal your private key. With symmetric keys identity is a pairwise arrangement. I may have an adequate handle on who you are but I cannot Identify you securely to John so that John can compare my designation of you with some other designation of you. Furthermore John can do this comparison off line — he need not consult the two candidates to see if they are the same, even if there such a feasible protocol. You can compare public keys from different sources. I see no symmetric key analog. In the scenario of the presentation, if B is given access to C by both A and D, can B determine that these to versions of C are indeed the same entity?
It is not clear that it is necessary to solve this problem but its lack of solution prevents me from using familiar system patterns.