The biggest threat was massive blaze. If some house caught a fire, no one would be putting it out, instead, everyone would be breaking other nearby houses, to contain the fire.
“May 2014. House fires were comparatively less deadly in the sixteenth century than they are today. Even conflagrations that consumed whole neighbourhoods claimed few victims, for wooden houses burnt readily but slowly and few had many storeys.”
What I assumed they meant is that while your cause of death is less likely to be a building fire, in the event of a building fire you may be more likely to be killed. That is, the absolute probability has gone down, but the conditional probability has gone up. I dunno about the truth of it, but I found it an interesting thing to consider.
I'm pretty sure something similar is true for stairwell falls and drownings would probably be tempered by the prevalence of lifeguards in popular swimming spots, and signage warning of particular dangerous areas.