This isn't a legal action or enforcement action. Consulting an attorney is reasonable and prudent (as your incident may end up a civil matter with insurance, owners, student, or others involved)...but with regard to the NTSB, if you can show that your accident did not cause substantial damage or meet the requirements of the defintion of an "accident" as you stipulated above, then you can appeal directly to the Director.
Did the amount of damage fall outside the definition of "substantial damage?"
Substantial Damage
Damage or structural failure that negatively affects an aircraft’s structural strength, performance, or flying characteristics, and which would require significant repair or replacement of the affected component or system. Substantial damage excludes damage to landing gear, wheels, tires, and flaps. It also excludes bent aerodynamic fairings, dents in the aircraft skin, small punctures in the aircraft skin, ground damage to propeller blades, or damage to only a single engine.
Did the damage require repair to the wingtip, aileron, spar, wing skins, or other structure in the area? If so, you may well be a candidate for meeting the definition of substantial damage, which means that you experienced an accident, by definition.
Unless you merely scratched the paint on a fiberglass or plastic wingtip, then chances are the wing sustained some stresses, and this most definitely affects the structural strength of a major component of the aircraft. If the aileron was in any way damaged, the flight control system has been compromised (remember that many aircraft can't be flown until the controls have been rebalanced if
paint gets on an aileron, to say nothing of damage)...that would be substantial damage.
What is the extent of the damage? Did the propeller strike the ground? Engien sudden stoppage or overspeed? Gear issues?
What I'm getting at here is if you are going to appeal, be sure you can show clearly that no substantial damage exists. The definition is purposely left vague in living document fashion, to be adaptable to various situations. It also leaves some room for discussion and flexibility...but you will need to be able to
clearly show that your evoloution falls well outside the boundaries of the definition. If you feel your case is strong enough, and you can gather together pictures of the damage, mechanics statements, bills for repair, statements from the student, the NTSB prelim, whitness statements, insurance paperwork, and anything else available to give you a solid leg to stand upon...then have at it. With investigators having already glanced at the matter and made a preliminary wave at "accident" classification, the ball is now in your court to make a case and prove that it's not an accident...that's best done with too much evidence than not enough and that's going to require leg work on your part.
Good luck.