I disagree with you but won't argue any further… Anyway the point is here that quiche is not the COD of faire alone…I disagree with your explanation, Maître Capello. Quiche is the COD of faire rechauffer, and NOT of rechauffer.
faire rechauffer is a causative construction which does not take the agreement. See: http://french.about.com/library/verb/bl-causative.htm
I hope that link can clarify things for you, pHOeBeBB.