Here's what NaS means. Suppose that you have a chain C1, and then some attacker with P portion of network hashpower decides to start trying to fork your blockchain starting N blocks ago. Then, there are two competing chains, C1 and C2. Now, look at it from the point of view as an ordinary forger. You have four options:
1. Try to forge on neither chain.
2. Try to forge on C1 only.
3. Try to forge on C2 only.
4. Try to forge on C1 and C2 simultaneously.
Because there is no significant cost to forging that is external to the blockchain, like there is with PoW, (4) is an actually viable strategy (in Bitcoin, (4) would have cost you 2x as much mining power). (4) is clearly the best from a revenue standpoint, because it gives you a reward if either chain ultimately wins, whereas the "honest" strategy, (2), gives you only rewards if C1 wins. Hence, all purely self-interested forgers will forge on C1 and C2, altruists will forge on C1 only, and the attacker will forge on C2 only. Thus, in order for the attack to win, the attacker will need to overpower only the altruists, not 51% of the entire network.
You guys are secure now because everyone is using the default client, which I presume enforces the "forge on C1 only" rule. Later on, clients designed and downloaded by users motivated solely by financial interest may well switch to double-forging. An analog of this problem exists for every PoS system to date with the exception, as I described in my article, of permanent-genesis-nobility and TaPoS.
