Your claim that attacking a PoS coin is a "fixed cost" and attacking a PoW coin is an "unbounded cost" is similarly ridiculous considering the costs of attacking both types are dynamic (PoS depending on the price of the coin and PoW depending on the hash power of the coin.)
It is absolutely correct. Once you control a PoS coin, you control it forever at no additional (significant) cost. How can anyone else ever take control away from you since you control staking and the only way anyone else can get stake is by buying it from you? No one can and you don't need to continue expending resources (mining) to retain control as you do with PoW.
Wrong. If someone buys up 50%+ of the currency supply to attack it, the PoS coin's community thanks them for the donation, forks the coin, rolls back the blockchain, and continues business as usual.