It goes way back than to 20th century (contrary to BBC story), apart from the very early pioneers for each given place of settlement boundary, the americans never much walked at all afterwards! That's the key 'missing' issue, the whole paradigm, why people left Europe in the first place: yep freedom of faith/religion, but also freedom to much higher personal consumption and resource exploitation, keeping large personal bubble, horses, cariagges, trains, streetcars, cars, airplanes.. etc.
Simply the ratio of school children and workers at any given point in time doing actual walking (and per range walked) was always less for the NA.
Large chunk of Europeans have no prob even today walk 5-10km daily (sun or snow), well guess what, because couple generations back, most of their ancestors naturaly did just that in order to get to and back from work/school/church and other activities.
It's like pushing the genie back into the bottle, can't fit.
To reverse the trend or we could say counter the 'over-specialization' of U.S. inhabitants has not been desirable, and is not likely possible now, only few exceptions to that rule apply, those various hipster 'new urbanism' city center revitalization projects here and there..
Is it possible to 'unlearn' such disease?, definately possible, but certainly not in the time frame of years or few decades..