I pursued this line of reasoning in the thread, but it turns out it is a FAIL. It turns out that Satoshi was correct. You either need publicly validated transactions OR you need to save the entire transaction history so the receiver can validate a private transaction.
The reason eluded me at first, so it is not stated yet in the thread. In private transactions, if you send the money to yourself you will own both sides of the verification. As such, you can increase the values to be anything you want. Nobody else is watching. If you throw away the history no one will know. You can now pass on your inflated money to anyone. FAIL. Doh!
So the amount of validation required before you can purge the history is greater than a private transaction. It may not require a full public broadcast, but if it does we've added only minimal privacy. (see earlier in the thread)