The question is, can you occasionally say fake a fork like this in say 5 minutes with a large enough percentage of network resources that the network accepts and uses to overwrite the 10 confirmations of a blockchain which cheats the system and overrides that calculation?
This is not "Nothing At Stake." That is an attack which can only work on a Proof of Stake currency (I know NXT has some defense against this.) The idea is that since the mining process verifying the blockchain only requires a commitment of the currency the blockchain is tracking, it costs you nothing to mine on all current forks, giving a forking attack a substantial advantage. That can't happen in a mining process which requires an economic commitment external to the blockchain. Buterin is the guy to read about this.
Why is there not a need to wait out deadlines? Is it possible to force that and make blocks, and therefore chains containing them, that have not waited out the deadline invalid?