I know people who have gotten singled out for verification before (it is a somewhat random process, she was told--her parents had really few assets, which she ended up having to document at length.) I don't know if there is punishment involved if you outright lie (like they take away all of your aid instead of just adjusting it down).
As far as I know, most people don't lie. It is fraud. Lying to the government is a bad idea. If you get aid that you don't qualify for, it is stealing. I think most people realize that they shoud not steal money.
Yes, completing financial aid paperwork is a royal pain.