Any blockchain is designed for to determine chronology in a distributed manner. The use of the word ‘timestamp’ in a PoW system is flawed, but chronology is certainly true. Each block comes out in succession, so that one can determine which coins were spent first and double spending is impossible. So the question is more about how PoS determines chronology.
While PoW supporters see their chain as objective truth, it is certainly possible to fork a PoW protocol. This is because they rely on a subjective choice of protocol rules embodied by the client. Indeed, when doing a fresh download of the chain, it’s not like you are recalculating every block from scratch. Rather, you download the chain from someone else and check it against hard checkpoint hashes hardcoded into the client software. So the question isn’t how do you know you’re on the right ancient timeline, as PoS and PoW both do that with hard checkpoints. The question is how do you know you haven’t split off from everyone else or that the most recent entries are false.
PoW achieves this by using computation as a scarce resource. PoS uses ownership over the established ancient timeline as a scarce resource. This is why distribution is so important for PoS, to bootstrap a self-consistent system. PoW does not need bootstrapping, but will inevitably become extremely cost-intensive by consuming exhaustible resources for temporary gain (unless we’re discussing something like primecoin, but that’s another story). Peercoin bootstrapped a solid historical timeline using PoW, then uses ownership over that timeline as a scarce but renewable resource to determine truth of chronology.
Ultimately, we agree that if you cannot trust the distribution, you cannot trust the chronology. But we believe that the computational power of PoW is destined to become more centralized with time, while the stake distribution of PoS will remain dispersed, assuming a good initial starting point. As an addendum, it could be argued that as PoW systems centralize, if you were to start a new coin like Peercoin that uses PoW to bootstrap, it would no longer have a trusted distribution. The trust implied by Peercoin’s historical ledger combined with it’s PoS security method may be less reproducible by the day, as PoW begins to fail as a distributed consensus mechanism.