I have huge issues with that reasoning, mainly because a hacker can get dirty coins onto an exchange before the hack is even made public, and thus the second exchange would have no idea they'd allowed a deposit of stolen coins.
My biggest issue with this is the privacy implications it has. He is basically saying that all exchanges must turn in to Big Brother, monitor all their customers, perform constant blockchain analysis on all their transactions, trace every satoshi they deposit, and ensure that every deposit is entirely "clean" and "untainted", all because he did something so monumentally stupid as to use a flawed and buggy web wallet to hold all the deposits to his exchange. If you can't be bothered to do the smallest amount of due diligence, then trying to turn bitcoin in to a nanny state isn't going to help you.A quick internet search seems that their Twitter is still active, so this hack doesn't seem to have shut them down. I also found an interview from a few days ago with their co-founder, with some very concerning lines in it:
Due to our huge amount of transactional data on cryptocurrencies and national currencies, we can now enable governments to understand things better and develop a positive outlook towards the industry. It will enable regulators to stop frauds or system compromise by following our compliance policies.
Sounds very much like they are sharing customer data with governments. I suppose that fits well with their "no privacy" ethos as described above. 
