Is "Business Accounting for Dummies" (as recommended in the accounting video) really the best book? It looks like it's meant for the UK, as well as being both out of print and not very highly rated on Amazon.. Maybe you meant "Accounting For Dummies"?

Your theory seems reasonable to me, and I know you're not defending them, but ...

How difficult is it to keep the right amount of bitcoin and USD in deposit? It seems pretty simple to me. Customer deposits $1.00, then I keep $1.00 in deposit in my business account. Customer deposits 1 bitcoin, I keep one bitcoin. The account for customer deposits will only ever be touched by automated systems processing these transactions.

If I'm charging fees as part of depositing/withdrawing/trading currencies or BTC, then those fees are immediately swept into a separate account, the entirety of which is revenue. Kept strictly separate from deposits. I'd regularly audit both accounts to confirm that the dollar amounts of each deposit/withdrawal, as well as total, match the records of actions in my systems.

Mt Gox only ever handled about 40 trades per second. Seems like you could keep everything balanced with a typical database, using transactions to implement atomic trades / deposits / withdrawals. Perhaps interfacing with money transmission systems is slightly more difficult, but once a transaction has reached the point of having probably-completed, you initiate the transaction to modify the customer's balance of bitcoin and currency.

So I guess I'm agreeing with you that if they failed in this way, they must have been incompetent.

P.S. I'm just making all this up. I've never worked in payments or accounting. I expect a good security or finance auditor could suggest much better controls. I'd pick up an "accounting for dummies" book and learn about the basic control principles used in accounting to prevent fraud. Perhaps I periodically download statements from my bank, print them out (or receive them in the mail) and audit those records against my own systems, by hand. Do the same electronically on a continuous basis. Set up an off-site write-only logging system to capture all transactions, and regularly audit to ensure that the system logs match bank transaction logs.