Touche. We don't know all the facts here. OP does not mention whether the mother and father were married. If not.. (from the DOS link I posted above)
"Birth Abroad Out-of-Wedlock to a U.S. Citizen Mother:
A person born abroad out-of-wedlock to a U.S. citizen mother and alien father on or before June 11, 2017, may acquire U.S. citizenship under Section 309(c) of the INA if the mother was a U.S. citizen at the time of the person’s birth and if the mother was physically present in the United States or one of its outlying possessions for a continuous period of one year prior to the person’s birth."
If the parents were married, then what you posted applies.
Either way though, as OP's mom did not seem to have lived in the US at all, OP is not going to be able to acquire derivative citizenship, so this is all moot.
And no, OP, there is no provision in American immigration law that I know of that allows grandparents to take the parents' place (unless maybe if the grandparents formally adopted you before the age of 16). Perhaps you are thinking of another country's law.