Yes, I think you've got it right. If the IRS does not consider it to be income, then its not income. Since all that's left at this point is an amount of cash, it seems that the cash will be reported on the fafsa as an asset in a savings account.
Your query on 'what if someone asks how we lived', it sounds as if you lived from a gift that you received during a tough moment. That's really not the same as money earned or an income from a profession.