Permissioned ledgers will face the same problem that was addressed and solved by the BTC system: how to prevent double spending and altered ledgers. It seems to me that permissioned systems could actually be viewed as being specifically designed to permit double spending and altered ledgers, outwardly for perfectly legal reasons while necessarily creating the theoretical danger of a hack.

Why? Because the 51% problem would be built in -- all the "miners" would presumably know each other and under certain circumstances could alter the complete ledger --- unless hashes of that permissioned-ledger were used to create a bitcoin address and a fraction of a BTC were sent to that address. If that were done frequently enough, then there might be no need for permissioned-ledger miners at all -- each hash would not have to have a series of zeroes in front of them, the way that BTC blockchain hashes do. Instead, each transaction would just be hashed once and then instantly sent to the BTC blockchain. Each such hash would be used in the next hash, etc., thus creating, in effect, a non-mined unalterable permissioned blockchain. Transaction confirmations within the permission system would be instantaneous. Also instantaneous would be the publication of each hash's bitcoin address on the BTC blockchain as an unconfirmed transaction. Since the purpose of creating the address in question would just be proof-of-existence rather than initiating a commercial transaction, confirmation time would be irrelevant. It could be done in snail-mail time.

Ultimately I think it comes down to this: if permissioned ledgers hash their data, where will such hashes be stored? In private or in public? If they don't hash their data, that would make their permissioned-ledger no different from a shared database -- which is the point raised in the Casares article.

Banks, reluctant to participate that closely with the BTC system, may initially opt for a middle solution: their own approved miners hashing to a level of difficulty that does not slow confirmation times too much.  Perhaps they would be paid by some kind of BankCoin token. But again the problem arises of the miners knowing each other, or at least having their identities stored in a centralized location that could in theory be hacked or opened illegally.

Thus will all permissioned ledgers lead to the BTC blockchain. It's just too useful to ignore.