The story is not true . A unmarried couple living together is treated the same as a married couple .
Now it is true that a couple gets less long term help than a single parent . Because they have no excuse to not have one parent working . A solo parent cant watch the kid and work at the same time .
Government doesn't check into people living in a household. One of the long-time welfare scams was for a woman to apply for welfare claiming her husband left her with the kids. He didn't go anywhere, he still lived in the house and there was no breakup. It's just that a woman was applicable for welfare because of her claim he left her.
A couple of years ago, I had to evict a family from one of my apartments. It was an unmarried couple. He worked, but she stayed at home "supposedly" home schooling her two kids even though she was a dumb as an ox. They kept getting further and further behind on rent, so I addressed them of the problem.
I suggested that she get a part-time job on weekends to catch up on the rent and maybe get ahead in life. She didn't even entertain my suggestion because she was getting $250.00 a month in food stamps for her and her kids.
If they were married, she probably wouldn't be getting that benefit and probably would have went to work to save their home. Long story short, I had to evict them.