What causes dreamers to accept dreams as reality?
If you are searching specific part of the brain, I think that frontal regions of cortex will be an answer(In particular, the dorsolateral prefrontal cortex which was associated with self-focused metacognitive evaluation). But, as it common in real life, becoming aware of dreaming state required coordinated work of different parts of brain.
You can read this very good article and wiki of course.


  Lucid dreaming is characterized by a regaining of higher cognitive capabilities, eventually leading to the awareness of the dreaming state. Recent quantitative EEG data have shown that this wake-like intellectual clarity is paralleled by neural activations in frontal and frontolateral regions. Likewise, PET data show cognitive control in dreams to be associated with activation of frontal cortex components. via