Earlier quoted context omitted.
It's not a contradiction, because 1) the webserver would not have login credentials to the hardened machine and 2) the interface would be much smaller than "everything in SQL". A typical example of such an interface would expose about four operations: // Return true if the given user/password pair is valid. bool PasswordValid(string user, string password) // Return true if the password was changed successfully. bool…
That'd still be 'internet-facing' though, by your definition. Yes, it might require one more round of cracking (the simple interface), but the machines are still connected.
Additionally, I object to your implication that any network service can be trivially compromised with "one more round of cracking". This is a view of software security that is propagated by science-fiction movies, and is not grounded in real life. Vulnerabilities that permit remote code execution are relatively easy to prevent by taking appropriate precautions when designing and implementing a network service, and almost every such vulnerability has its root cause in doing something obviously insecure (e.g. writing in C/C++ or a language with eval(), passing user input into an OS procedure).