That's how it should be architected, but the article shows that Cox's network gives no thought to security so it's unlikely how it is architected. Even if the Cox answer is correct to the best of their knowledge, we can't rule out that attackers are inside the network wiping out their logs.
You’re right, except I’d say that Cox gave some thought so security, but not enough. Which is in some ways even more dangerous than ignoring security entirely.