A thought. It is known that when one eats peppers and needs to tone it down, you eat dairy products to absorb the oils from the peppers that were deposited in the mouth so that they can be taken on down to the stomach and not burn the mouth anymore. Knowing that water and oil do not mix, letting the little one drink lots of water (which we all know she wants to do because her little mouth is on FIRE!) isn't really going to solve anything other than cooling it down a bit. My thought is this. Wonder if you were to let her have a little bit of peanut butter or something that would coat her mouth just a bit and help to absorb lots of those oils that are in her mouth and let those nasty oils get on down to her stomach? What kinds of horrible things would happen from that?
Side note...my dad when he was a child (he's a pharmacist now! hehehe) once bit into a hot pepper on his parents farm and took off to the house running! When my grandmother found him, he was standing in front of the refridgerator with a stick of butter in his mouth!

THAT'S where this "old wives tale" came from. FYI!