How is domain privacy relevant here? That only hides your email from public records. What if the attacker already knows it (as they did in this case)? Email address is quite literally something you are meant to share publicly. It is not a password.
Registration info usually also includes a physical address and names.
I think their point was that if WHOIS data were hidden, a password reset request that relied on providing the email address would've been impossible. But since NC's account management allows visitors to provide just a domain name to generate an unlock email, domain privacy wouldn't be a protective layer here.