It's a common line of thinking that a system is broken if there's a single instance of failure when the right measure is if it does more good than harm. I've heard that excuse in the US with regards to giving to the poor, "they might waste it on booze and drugs." Well sure, but they might also use it to keep from starving.

In this case, are there some people that "don't deserve it"? Certainly, but there's probably many more that do who are making use of the program. Adding overhead and bureaucracy to try to weed out the undeserving may very well make it so fewer people who need the assistance get it. It's human nature to overweight small negative outcomes while underweighting the larger good. You need to objectively study the problem to fully understand where the tipping point is which rarely happens because these types of things quickly become political.

I don't personally know enough about this particular topic to speak to it, but the general answer to the question

  > How hard is it to disqualify them due to financial means?

Is it's harder than you think without undermining the original goals of the of the program.