There's a reason the occasional mandatory workplace-safety education sessions you have around your office focus on things like ladders and picking up packages: people actually do those things.
Postscript: Also, auto accidents cause kill more people in the US than terrorism. :P
With or without encouragement by their employer, they would have a pretty clear worker's comp claim, as the injury is "in the course of employment."
Also, I would imagine that the company promoting usage of stairs has had an actuary do the cost-benefit analysis of the potential health-care savings versus the potential worker's-comp payouts.
Doing this sort of analysis "right" (trying to determine which drugs are least-bad, quantitatively) would be a daunting challenge.