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Well, the sodium-potassium pump keeps the outside of the cell + and the inside -. At the resting potential, anions would be inside the cell to maintain +/- aspect. During an action potential it is primarily the movement of sodium and potassium that changes the relative charges inside/outside the cell so i imagine they would stay put.
So yes, I am incorrect that extracellularly there are more Cl, however this is adjusted to maintain the resting potential. Also, the negatively charged anions that result mostly from proteins intracellularly help maintain the -70 mV resting potential as well.