It may be the case that identity is part of any contract dealing with property by logical necessity (since property cannot exist but with the identity of the proprietor - you can't go to the bank and ask for your money if you refuse to identify who you are even if it is in fact your money).
This is surely not the case. GLBSE did not know the identity of the users, so this information cannot be used for authenticating the request against gigamining.
The bank also only needs this information because you proved your identity to them when you were opening an account in the first place, and there also used to be bearer-instruments. Due to stupid laws, these have been to a large extent eliminated, but when I was younger, there were bearer passbooks.