We can't open the box and see what is inside directly, but we do have more info than we do about other people. We have partial access to the outputs of different parts of the brain.

We can simulate how we'd respond in circumstances in addition to the circumstances we actually find ourselves in. Of course, we can think we're simulating what we'd actually do but actually simulate what we think we should do, but that's a self deception problem and not a problem fundamental to introspection.

For example, I can ask someone "Why did you buy that car?" and they can answer the first thing that comes to mind (which may be wrong, and may be selected because it makes them sound good), or they can think "hmm, would I have felt the urge to buy the car if it was not blue? No? I guess color was important"