There's likely contaminants on the surface of the battery which, when water is added, become conductive.
if youve ever rubbed pH paper on an auto battery youll realize there is a lot of residual sulfuric acid on the outside of the case.
That mixed with water is pretty conductive.
Yeah humidity increases the conductivity of air by reducing the breakdown voltage of air, not by conducting electricity, because it doesn't conduct electricty, because it's an insulator.