As a practical matter, it is very hard to prove that "X person has not given me any support" especially if the support was given off the books.
I don't think this is right (there should be exemptions when the parent refuses to pay) but it will probably cost a great deal of money (taxes) to check references .. let alone references that you never gave.
Even funnier course, independ students can still have parent support but get the grants/loans that you can't have.
BTW, you are independent if:
You are 24 years of age or older.
You are getting a masters or doctorate degree. (huh???)
If you are currently married. (Not sure if this applies if you were married, but are now divorced; and still under age 24/)
You provide support for children or other dependents. (Technically, they must recieve more than half of their support from you.)
You were an orphan/ward of the court (in foster care) until You turned 18 (or you still are a ward if you are currently under 18).
You are a veteran of the armed forces. (This applies if you went to academy but withdrew in good standing.)
So, some easy ways to become independent: wait until you turn 24 before going to college, get married, have a baby (and raise it), or join the army and go to college after you finish your tour.
[Obviously, these are hard enough that it is unlikely that anyone will do them just to change their classification. Waiting until you are 24 is the easiest and most reasonable, joining the army is equally reasonable (but harder).]
Supposedly, there are other ways to be classified as indepedent as well (these are lumped together as "extenuating circumstances") but I have no clue what these would be. Mere parental refusal to pay is never a good enough reason, though.