Yes, the trick to getting stains out of a ceramic teapot is salt. Dissolve several tablespoons of salt in hot water, fill the teapot, and let it soak. An hour or so later, come back, dump out the salt water and your teapot will be nice and clean on the inside, and no chemical residue or aftertaste.
We have a stainless steel coffee maker carafe, which isn't really stainless! I wonder if the salt treatment would work for it.