Has Gox actually said this? Doesn't seem clear who the author is.

Whatever the supposed mechanism is, it doesn't make any sense.

You should be able to calculate how many bitcoins your wallets control. Maybe there were some fees you didn't take into account, but it should be close. Then you see how many your wallets actually control. If the total is way off, you investigate, same as any other business that checks its cash register at the end of the day.

This document suggests that no one made that simple comparison for years. It's preposterous.

It would be like McDonald's declaring they ran out of assets because the cashiers kept giving out money due to an error in their protocol, and this lost cash was continually replenished from McDonald's corporate bank account. That's what the document purports.