Every person with Mexican nationality is legally required to declare himself/herself as a Mexican national when entering and leaving the country (Art. 12 Ley de Nacionalidad). Mexicans who hold other nationalities and that enter or leave the country declaring themselves as foreigners can be fined with anything between around 21000 and 35000 pesos (Art. 33-I Ley de Nacionalidad), so OP you should never identify yourself as a US citizen when entering or leaving Mexico.

Mexicans don't need a passport to enter Mexico. A passport can be used, as well as a matrícula consular, voter card, certified copy of birth certificate and other documents that prove Mexican nationality (Art. 36 Ley de Migración). Foreigners are explicitly required to enter with a valid passport (Art. 37 Ley de Migración).