There's at least one pretty fool proof way to defeat this specific kind of fraud. Give tuition waivers rather than grants.
Or, of course, just charge less. I went to LA City 20 years ago. Had a bad experience unrelated to school itself at the first four-year I tried to attend and had to drop out. My parents couldn't actually afford to send me back, but the reported income was still over the threshold to get me enough aid to afford a four-year. So I started at a community college. It was $9 per credit hour at that point. Financial aid was not necessary. I just worked an overnight shift detailing the restrooms at Knott's Berry Farm theme park.
Or, of course, just charge less. I went to LA City 20 years ago. Had a bad experience unrelated to school itself at the first four-year I tried to attend and had to drop out. My parents couldn't actually afford to send me back, but the reported income was still over the threshold to get me enough aid to afford a four-year. So I started at a community college. It was $9 per credit hour at that point. Financial aid was not necessary. I just worked an overnight shift detailing the restrooms at Knott's Berry Farm theme park.