My DS turned down scholarships as well.
ALL of them stipulated that they could NOT be awarded if he was appointed to a Service Academy.
Here is what the National Eagle Scout Association says (for instance):
"Attendance at U.S. military academies is paid by the U.S. Government. These scholarships are typically worth $400,000 each. Additionally, attendees receive a monthly stipend from the U.S. Government. These students have secured an education. Other Scouts might not be able to attend college at all without receiving a NESA scholarship. Our goal is to help as many Eagle Scouts as possible to attend college."
The $400K thing seems a bit inflated, but there you go. It's an example.
Back to the original intent (I think) of Capt MJ's post, though: DO fill out the FAFSA form, because everyone should have a "plan B", in case they don't get into a Service Academy or ROTC program.