Caffeine doesn't actually do any of the things sleep does to your brain. If you drink coffee during a late night, you won't feel as tired, but your brain performs worse, your reflexes are slower, you're less likely to remember things, etc. It's like painting over a rusted car instead of properly maintaining it, basically.

I think GP was just making a point about the fact that “tired” is a subjective experience, like pain. Arguably, if you’re on pain medication, you’re not in pain, even if your body is sending pain signals that your brain just isn’t receiving or paying attention to.