Is TEFL document authentication needed (by the Chinese Embassy)?

Is TEFL document authentication needed (by the Chinese Embassy); since the school where it was obtained is in Mexico? I am an American citizen and will have my 4-year degree and background check authenticated at the Chinese consulate in the USA (however; I will not fly to Mexico just to get a "stamp" (and was told that ONLY the Government Office in Mexico City can "legalize"/authenticate THIS document).