They made a choice: Sell the Mercedes (likely for $8,000 - $12,000 in cash) and support their family by supplementing their income for six month to a year on that, less after buying a $3000-$4000 daily driver. When you're in food-stamp-hyper-frugal-mode, $8,000 cash can keep your family alive for some time!
They chose to get food stamps and keep the luxury car instead.
It was their choice, but when you're driving around your "emergency fund" and your bank account is hovering at zero while Uncle Sam puts food on your table, some would suggest your priorities and means are a bit confusing.