Yea thats totally bs on them and it shouldnt even be an issue.
Next step, contact your House rep. Most are often glad to try and help for things like this. Especially if they are vets themselves. For others more political than anything else but 'fix the VA' is popular. Might require doing some kind of appeal first, if they have a method for that. The bureaucracy wants your money but wont give it up unless they have to or it makes them look good. Income or not. Taxes paid or not. Not to us so much. But to those that control the money they get. Your rep also wants to look good to the voters in your district.
I have to tell you however that you are wrong on one thing. Taxpayers SHOULD help subsidize vets in one way or another when it comes to things like housing. At one time they did without asking too many questions. You risked your life for your country so they didnt have to. You werent simply a govt employee. They should at least help you when it comes to getting a place for your family to live in.
There was an interview I saw a long time ago of a woman in the army that was deployed to the ME after 9/11. She said she signed up mostly for the benefits. Things like help with college. It was a good deal. She also thought that, keeping in mind the times, we wouldnt be going to war anytime soon. But I didnt look at her situation as a negative because when push came to shove, and the time came, she went there without hesitation to do her duty instead of trying to find ways to get out of it. The govt... and the taxpayers... have their own duty to support and help her.