That's simply not true. It's a misreading of the USDA's food security survey results, wherein the standard for "food insecurity"[1] is
[R]eports of reduced quality, variety, or desirability of diet. Little or no indication of reduced food intake.
Note the second sentence. Hunger is not a "reality" for your family just because the USDA judges you to have "low food security".
[1] http://www.ers.usda.gov/topics/food-nutrition-assistance/foo...
http://www.ers.usda.gov/publications/err-economic-research-r...
From your link, of those that reported "very low food security":
96 percent reported that an adult had cut the size of meals or skipped meals because there was not enough money for food.
89 percent reported that this had occurred in 3 or more months.
95 percent of respondents reported that they had eaten less than they felt they should because there was not enough money for food.
68 percent of respondents reported that they had been hungry but did not eat because they could not afford enough food.
47 percent of respondents reported having lost weight because they did not have enough money for food.
29 percent reported that an adult did not eat for a whole day because there was not enough money for food.
23 percent reported that this had occurred in 3 or more months.
*Edited for formatting of percent breakdown