When you question their 'definition', try and remember that the 'definitions' were designed by advocates.  

The larger the number and the wider the definition, the more money that can come from the government to be spent.  

And, for some advocacy organizations, the broader definition also helps drive their charitable 501c(3) income stream...some for good organizations, and some for 
'expenses and salaries' for the fat cats at the top of questionable organizations.  

The 'school' definition is written as broadly as it is in part to get more free or reduced lunches (and breakfasts) for kids in the local schools.