As I recall, that system's security claims assumes that the users have a synchronous network-- every message is reliably delivered in order to all users.  This is a rather nonphysical assumption, the only way we know how to construct such a thing is to use some kind of consensus system. Which would make the name "Ouroboros" rather fitting. :P

If you did actually have a synchronous network, you wouldn't need any kind of POW/POS whatever, you'd just have people send their transactions and the first one sent wins. As a result under that assumption you could prove virtually any kind of system secure, even ones with absolutely no security in the real world.

Because of the long history of unclear, misleading, obfuscated, or outright dishonest claims about security from people promoting POS and other alternative consensus systems, I think most experts have for the time being run out of patience reviewing these things.  I'd like to suggest that anyone who thinks they have a really good framework would do well using it to prove similar alternatives like stellar, ripple, or ethereum's-r&d insecure. I say this for two reasons: One is that if someone's framework can't prove other systems insecure, then why should we expect it to tell us if their new system is insecure? The other reason is to escape from an unscalable behavior where poorly considered schemes are thrown over the fence and saturate a limited number of people who can review them.  I also think that the best informal evidence that someone is qualified to build a system is that they're able to find flaws in other systems, and without something like that its simply too hard to prioritize review over other work. This sort of activity can help clarify what properties a proposal is actually providing.