The answer here is "Well yes, but actually no."

Those PSAs assume a generally sedentary lifestyle typical of the middle & upper classes. Owning a detached home away from urban centers, driving everywhere, and working a desk job, that kind of thing. If you live that kind of lifestyle, then you will have to actively count calories, and do extracurricular exercise in order to stay healthy because you won't be doing enough physical work at any other point in your life in order to do so passively (and this is before we get into matters of diet composition, which is another thing entirely).

This is also why the biggest assholes who insist that obesity is a personal failing, and not a structural problem are almost always middle class strivers, or those looking to join their ranks. They're fully aware that attacking the actual structural causes of obesity means attacking their accustomed lifestyles, and they don't want to do that.