I am, however, still curious what good proving ones identity is going to do. There are no identities connected to these accounts to begin with, so no way to prove that John Doe's coins are his even after he proves he truly is named John Doe.
It has nothing to do with ensuring that funds are returned to whoever deposited them. It has everything to do with knowing who receives those funds. In taking those funds without at least minimal KYC information from users, GBLSE was allowing and encouraging people to bypass AML/CTF requirements. Returning those funds to users without gathering at least a minimum amount of information to show where those funds have been disbursed to would only compound any offences GBLSE has already committed.
If that's the case, then wouldn't all of those who sent money in to GLBSE be facing the same charges? Afterall, how many of us have any idea who Nefario is? Not to mention who is on the other side of the securities we purchased.
The obligation is on the providers of financial services/products. Yes, you can be charged if you're using GBLSE to launder money, evade tax or finance terrorism but in general the user/purchaser of a financial service/product doesn't have AML/CTF/KYC requirements. Of course if the operators have publicly made statements making clear that they're in some way operating illegally and you choose to deal with them with that knowledge, you may be leaving yourself open to charges.