On second thought, I'll add that the money quote would be even more persuasive if it were true.
Bangladesh life expectancy: 70.3 years (as of 2012)
First hit for "Appalachia life expectancy" is a page that cites the Washington Post. On that 2011 interactive map I find a few counties that give life expectancy for men below 70 years, but the women's number pushes the average over 70.
The source is "Institute for Health Metrics and Evaluation at the University of Washington" where I find a gloomy article with this worst-case-scenario:
Five counties in Mississippi have the lowest life expectancies for women, all below 74.5 years, putting them behind nations such as Honduras, El Salvador, and Peru. Four of those counties, along with Humphreys County, MS, have the lowest life expectancies for men, all below 67 years, meaning they are behind Brazil, Latvia, and the Philippines.
If "below 74.5" means 74, and "below 67" means 66.5, and these numbers both apply to a single county like Humphreys (population 18,538), then the average is 70.25, about the same as Bangladesh as a whole.
But who cares about facts?