muriatic vs. sulfuric

He's wrong. Lowering the pH of the water changes the form of some of the carbonate in the water to carbon dioxide, which reduces the measured alkalinity and makes it possible to remove it from the water by aeration. It doesn't have any permanent effect on the alkalinity unless you aerate the water to remove the CO2The alkalinity doesn't care how the pH got lower.

Muriatic acid contains hydrogen and chlorine, both of which are normal in a pool. H2SO4 leaves sulfur behind.
 
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