The oxidation of hydrogen sulfide into sulphuric acid is a slow process. You can fill a room, or in this case a car, with deadly amounts of the former, and that enclosed space will remain toxic from H2S for hours and hours.
It is instructive that the reports says the battery in the car was the battery with which it was sold, but it is not clear whether it is an original equipment battery.
Since I know that hydrogen sulfide poisons the olfactory nerve first, it's been my policy both when working as a chemist, then as a waste-water chemist, and finally in a photographic darkroom, if I smelled hydrogen sulfide, I got out of there before it could overcome me. Now that YOU are educated, if you smell it, you know something is badly amiss, and you should get out of there, too.