Like @Traktion said, it all depends on how those 32 are decided upon; you can’t do much if you have no knowledge of or control over who’s in the quorum (i.e. whom to hack, bribe, etc.)
This ledger is just a web of certificates about arbitrary documents; if some (or most) of those documents are Safecoin transactions, so be it. It’s like colored coins, in a sense.
However, some could tie the ledger to external references, such as Bitcoin blocks, or blocks of other blockchains, or they could be timestamps by “trusted” entities (but everybody can decide whom to trust, so: no pressure, these are just random pieces of data, until somebody cares about them.)
That was in the context of entering a document about an already quorum verified transaction; if we already established the validity of a transaction (i.e. “X transferred Y N coins”), then all what’s left is to verify when it was done. In the absence of a globally trusted timestamp, that is only possible in relation to other things (but the blockchain does the same.)
I don’t claim this system will give you blockchain level confidence about the ordinality of all transactions, but I argue that it is not necessary in most cases (contributes to bloat), and unwanted in many (compromises privacy). In the cases when it is required by the parties for personal, business, legal, or any other reasons, they can just agree to use the ledger; in this system, the public ledger is not the basis of the transactions, it’s just an add-on, a clerical tool. Again, like colored coins: nobody forces us to use them, but when I want to enter a certificate about something in the blockchain, I have the choice.