This is actually a question that's plagued me for a while. I had several discussions with professors back when I was getting my second totally useless graduate degree (kidding! - see link) back in Florida about the accuracy of using "free and reduced lunch" as a measure of student poverty.
The answer, basically, is that it's the best tool we've got. We don't go around and take surveys on students' economic backgrounds, because that would be expensive and intrusive and probably not much more accurate than using "free lunch" data.
But, once again, "reformers" like NJ Senator Mike Dougherty - who wants to distribute state aid equally, regardless of student characteristics - haven't thought this through:
Gee, poor people without supporting documents - what are the odds? Are we really prepared to spend all kinds of new money to deal with this "problem"?
This reminds me of the plan to expand testing to all different grades and subject areas just to have more (bad) data to "evaluate" teachers. Are we really going to divert some more of our limited resources away from the classroom and toward programs that only serve to make corporate reformers feel better about themselves?
Of course, Dougherty's plan would eliminate the need for any data on student poverty; if every kid gets the same amount of state aid, why even track where the poor kids are? In fact, he would probably sleep better at night, blissfully ignorant of the damage he's doing, if he didn't know how much money he took away from the kids who need it the most.