Your statement is true, but mainly because very few people in the US are actually starving. What they are doing is living on poor diets.

There certainly seems to be some kind of correlation between low income on obesity, but the contributing factors are complex. Individuals and families living on low incomes may lack ready access to fresh food ("food deserts") due to high transport costs and/or there being no nearby shops that sell it, may not have equipment to prepare food, may live in areas where opportunities for exercise are limited due to crime or lack of facilities. Poor education about nutrition and lack of role modes can also be important factors.

I'd urge you to read the short article "Poverty and Obesity in the U.S." [1] from the American Diabetes Association. Quote:

"How is poverty linked to obesity? It has been suggested that individuals who live in impoverished regions have poor access to fresh food. Poverty-dense areas are oftentimes called “food deserts,” implying diminished access to fresh food (7). However, 43% of households with incomes below the poverty line ($21,756) are food insecure (uncertain of having, or unable to acquire, sufficient food) (7). Accordingly, 14% of U.S. counties have more than 1 in 5 individuals use the Supplemental Nutrition Assistance Program. The county-wide utility of the program, as expected, correlates with county-wide poverty rates (r = 0.81) (7). Thus, in many poverty-dense regions, people are in hunger and unable to access affordable healthy food, even when funds avail. The double-edged sword of hunger and poor availability of healthy food is, however, unlikely to be the only reason as to why obesity tracks with poverty."

The American Society for Clinical Nutrition has a paper from 2004 titled "Poverty and obesity: the role of energy density and energy costs" [2] that goes into a lot more detail. From the abstract:

"A reduction in diet costs in linear programming models leads to high-fat, energy-dense diets that are similar in composition to those consumed by low-income groups. Such diets are more affordable than are prudent diets based on lean meats, fish, fresh vegetables, and fruit. The association between poverty and obesity may be mediated, in part, by the low cost of energy-dense foods and may be reinforced by the high palatability of sugar and fat. This economic framework provides an explanation for the observed links between socioeconomic variables and obesity when taste, dietary energy density, and diet costs are used as intervening variables."

I would urge you to look into this subject more carefully and, considering some of your other comments in this thread, to avoid resorting to crude and misleading stereotypes of people living in poverty.

[1] http://diabetes.diabetesjournals.org/content/60/11/2667.full

[2] http://ajcn.nutrition.org/content/79/1/6.full