That's actually pretty laughable, from a logical standpoint.
I didn't qualify when I had an intact female shepherd, even though we were waaay under the poverty level at the time. Why? Well, she was the wrong breed of course! But it's okay if people have whoops litters as long as they're shepherd and chi mixes. As long as it's not a bully.
The weird thing is they didn't have an income cap on it either. So I could have been making $100,000 a year and still had my bully altered for free.
If it was really about lowering the overall population of unwanted dogs, there would be spay neuter assistance for all breeds and mixes.