Association != causation. While the picture this caption is from is indeed ridiculous (grandmother driving her daughter essentially to the end of her driveway for the school bus), the implication seems to be that Americans walking less somehow has a causative effect in skyrocketing obesity rates. This seems entirely wimpy and facile.
Here's an alternative: there exists an underlying metabolic disorder that develops in a large proportion of the population, in response to something new in our environment ( new compared to pre 1950's ). A major effect that this disorder has is to partition a large part of our calorie intake towards fat storage. Now we have less energy available for expenditure, and as a consequence we either eat more or behave more sedentarily. Sedentary behavior will be a compensatory effect, that will indeed associate with obesity ( as measured by observational studies, like the one mentioned).
A good candidate for such malady would be insulin resistance [1] (and more generally, metabolic syndrome); Gary Taubes makes a very compelling case [2] that this is indeed the case, and that the primary change(s) in our environment to cause these problems is our marked increase in sugar and refined carbohydrate consumption [3][4]. The same hypotheses also seem a good explanation for rising type II diabetes rates.
Now this is still a controversial topic [5], but my point this kind of explanation seems much stronger and more on-the-mark, than such flaccid ideas like 'americans are getting fat because they don't walk to school anymore'.
[1] http://en.wikipedia.org/wiki/Insulin_resistance [2] http://en.wikipedia.org/wiki/Good_Calories,_Bad_Calories [3] http://journeytoforever.org/farm_library/Cleave/cleave_ch2.h... [4] http://wholehealthsource.blogspot.com/2012/02/by-2606-us-die... [5] http://en.wikipedia.org/wiki/Insulin_resistance#Causes