The Sunnyvale world doesn't strictly require supernatural explanations -- you could posit vampires as being a subspecies of humanity, etc etc etc. But as you said in that post, it doesn't matter; we don't really care if vampires are the product of demons or mutated genes. We just care 'does there exist a monster that appears human, and likes to drink blood? does buffy exhibit superior strength and reaction time that is useful for fighting said monsters?' The reality presented by the Sunnyvale world appears to answer 'yes' to these questions, while the reality presented by the hospital answers 'no'. It's something Buffy can look and see; the question is WHICH set of sensory inputs to trust.