How can a battery get reverse charged? (other than by being charged backwards)
Specifically, when cells are in series, the one(s) with the least current capacity (due to imbalances during manufacture, or uneven deterioration) will be reverse charged by the remaining  cells as the last few coulombs are withdrawn. In this state, the battery as a whole still would have a small net charge, as opposed to reverse charge... but then, over time, all the cells degrade. Perhaps those with a bit of remaining charge degraded faster, leaving a net reverse charge.
The interesting thing about Planté lead-acid cells is that technically, the chemistry is reversible, though modern cells are physically designed with pockets to hold lead oxide, so provide full current only in the forward direction.