So if I understand this, this is how it would work.

At any time you'd have two passwords: one regular, which you use every day; and one for one-time-use only, which you keep around in case of need.

When sitting at an untrusted computer, you use your one-time-use password. This proves your identity, but also immediately expires your one-time-use password. Next time you want to generate a usable one-time-password you'll have to login with your regular password again.

Is that it?