There's a key point that's being barely touched upon here, and addressed a bit more in the UX thread you linked, which I'd like to highlight.
The password confirmation field, on its own, does not serve any security purpose. However, it does serve as a usability supplement to ease headaches that might otherwise be caused by something that is a security function.
The reason we have users confirm their passwords is because they cannot see their password on-screen when they enter it. The reason we do not allow them to see the password on-screen is to prevent shoulder-surfers, security cameras, shared desktop users, and screen capture tools from seeing the password.
If the password field were to remain unmasked, then it would be reasonable to do without password confirmation. You can already see this in action in some applications (KeePass is one exampe) which allow you to selectively mask/unmask the password field. In those applications, the password confirmation field is only enabled when the password is masked.
The purpose of the password confirmation dialog is as a sanity check for the user. Users cannot be trusted to enter their password error-free 100% of the time, and much less so when they can't visually verify the password prior to submission. However, it is very unlikely that a user is going to "fat-finger" their password the same way twice in a row. This allows a user to be relatively confident that they are setting the password to what they think they are, without having to compromise security by displaying it on the screen.
Of course, it should be understood that this is only necessary at the registration phase. This is because you only have one chance, during setup, to set your password before you are committed to it. When logging in, you get multiple attempts. A one-time error at login is much less costly than it would be (without the confirmation field) at registration.