Folklore.
Auto batteries are lead acid. Specifically lead (pB) and lead oxide (pBO2) and dilute sulferic acid (H2SO4). Two units of acid combine with 1 each lead and lead oxide to form lead sulfate and water, releasing electrons. Charging reverses the chemistry. A depleted battery therefore has used up both its acid and its lead. Addition of more acid, either battery acid or aspirin, can give a temporary boost. But since there is no additional lead, it is TEMPORARY.
Blacksmith