"I read that they do not even pursue looking in to people claiming a need for Food Stamps. Aparently it's cheaper to hand them out and not even investigate."
The author you read was clueless.
Of course they look into their income and expenses for housing, utilities, etc.
"After applying, applicants will in all likelihood need to furnish extra documentation during an interview with a state case worker and fit all prerequisites set forth by the state on an ongoing basis in order to continue receiving benefits."
The "all likelihood" refers to people - and babies too - already approved for another program such as Medicaid. Those folks and their info are already known.