Maybe they do, I don't know, but why doesn't the WTBTS/JW help their needy, and the needy of other groups? If a JW family in need, and I'm sure there are a few, required assistance, could they go to a local Kingdom Hall and ask for it? Or drop by one of the local elders homes and request for a meal? My church sponsors a homeless shelter. If JWs, or anyone else, were to visit for assist or a meal, they would get it, no questions asked. Does the WTBTS/JWs do anything like this?
Well... there might be one reason that I can think of... this family is not 'spiritually strong'. That is - they may not make all of the meetings (all 5 of them), plus they may not be going out door-knocking, plus they may not be doing whatever JW-related activities that are required.
I can tell you this from personal experience... when I was still married to wife #1, there was a large family that had very little. The father worked - but made very little income. The kids were getting to their teen years, and were eating lots.
Anyway, when we would go shopping, I would ask the wife if we had enough money to get some 'extras'. She would check and usually reply 'yes'. (We didn't have _that_ much ourselves) So, I would grab an extra bag of potatoes or loaf of bread - or whatever.
We would then drop it by their house. Sometimes they wouldn't be home, and we would just leave it there. Funny - somehow, they seemed to know it was from us, and thank us for it later.
Anyway... we did this for a while, and the wife came home from one of her meetings (I was totally inactive - hadn't been for over 15 years), and told me that she was told that we couldn't do this anymore, as the family was 'weak' and wasn't attending meetings reguarly.
I respected her 'religion', and so we didn't do it anymore.
So... it wouldn't surprise me if the family being discussed in this post - who may have signed up for some 'aid' somewhere else - was considered 'weak' by the JWs.