I don't disagree regarding hydrogen, my remarks were directed to the OP's query as to what was causing the rotten egg smell. Hydrogen is of course another highly hazardous material, and as you rightly say, proper care is needed when handling any of these things.
However, risk is about probabilities as much as possibilities - certainly batteries *can* explode, and hydrogen *can* ignite, but just because something can happen doesn't mean it is in practice likely to. That begs the question, of course, of just what do we mean by "likely" to happen?
I don't have any statistics to support this, but I'd guess by far the most common accident with batteries is fires caused by sort circuiting the positive terminal to earth, setting fire to the cable insulation as a result together with personal injuries such as burns.
I can imagine simply dropping them on one's foot is another common source of injury.
Whatever the detail, you are of course absolutely right: it's best to be cautious with batteries in general.
PS: curious about your fitter doing the battery drop test - you drop test an acid-filled battery while it's being charged? without any protective screening or scrubber shower?

Is that normal?