The source on the "10x less risky than going down a flight of stairs" is https://static.guim.co.uk/sys-images/Guardian/Pix/pictures/2.... That shows that in the UK in 2010, 655 people died from falling down stairs. That translates to a 1 in 100,000 annualized risk from falling down stairs -- the relevant comparison is "10x less risky than using stairs a typical amount for an entire year".

Interestingly, running the numbers for the UK shows that the annualized per-capita risk of dying on stairs in the UK is more than twice as high as it is in the US.