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why didn't both read the same since the neutral was connected to the house ground?

The resistance of the soil around the ground rod is very high in comparison to the other condutors. This means that you can pretty much ignore the ground in the calculation.

The voltage in either leg is simply a result of the load on it. If you have no load on one leg, you'll have 240V to neutral on the other. If the load on both legs is equal the voltage vill be 120V on both legs.

The question is: Does the ground rod keep the grounded conductor at ground potential, or does the ground rod keep the ground at the grounded conductor's potential? Contrary to conventional wisdom, I hold the latter to be true.