Basically, yes. And so they’re asking you to prove that you’re not. You understand how implausible your situation seems. You own a home. Even if you own it outright, you’re paying property taxes, I’m going to guess, very conservatively, and amount that would work out to $100-$200 a month. You have to heat that home in the winter, flush the toilets and shower with some kind of water. The 4 of you need to eat and if your mom drives to work, you buy gas and have to pay insurance on a car. You all wear clothes and shoes. Your income is less than $1000 a month. You can see why the colleges would ask? Your expenses nodoubtedly exceed your income and it looks like that savings won’t last much longer.
You may need to have a conversation with your parents. There may be help from a family member or other source that you don’t know about. I’ve known people to live off HELOCs in dire situations as the interst only payments can be very low. Be as forthwright as you can with the school. There’s some discretion involved in putting together a fin aid package, for example making it loans heavy or grant heavy or leaving a huge gap. You need a huge FA package. I’d urge you to be very compliant with and respond quickly to all requests from the fin aid office.