But then good health and daily activity are the best ways of preventing falls, (along with balance training and physiotherapy, especially after a surgery or stroke) so yes it is a cycle as you say.
I don't agree with it being primarily a cultural thing though. Daily exercise is an individual choice. There's a guy in my new building who I see all the time, he just walks to the end of the hall and back many times each day. Each lap probably takes him 10 minutes. But he chooses to stay active, even in very old age.