No. The NTSB investigates significant accidents (either commercial operations or passengers involved.)
There's an average of 400 GA accidents per year, so about one a day.
If two CFIs climb into a Piper and crash, it probably won't be investigated. Add a passenger, then the NTSB gets interested.
Source: commercially-rated airplane pilot.
"The National Transportation Safety Board is an independent Federal agency charged by Congress with investigating every civil aviation accident in the United States and significant accidents in other modes of transportation – railroad, highway, marine and pipeline."
So if the NTSB is not investigating every civil aviation crash, then they are failing in their congressional mandate. If you have evidence of this, you should probably contact your congress person or a newspaper with the details.
> [1] Aircraft accident means an occurrence associated with the operation of an aircraft which takes place between the time any person boards the aircraft with the intention of flight and all such persons have disembarked, and in which any person suffers death or serious injury, or in which the aircraft receives substantial damage.
Substantial damage is then defined as:
> Substantial damage means damage or failure which adversely affects the structural strength, performance, or flight characteristics of the aircraft, and which would normally require major repair or replacement of the affected component. Engine failure or damage limited to an engine if only one engine fails or is damaged, bent fairings or cowling, dented skin, small punctured holes in the skin or fabric, ground damage to rotor or propeller blades, and damage to landing gear, wheels, tires, flaps, engine accessories, brakes, or wingtips are not considered substantial damage for the purpose of this part.
A planned landing in terrain, if it caused no injuries but caused enough damage to aircraft to prevent takeoff without repair, would be classified as accident, but its investigation might be very brief depending on the event in question.
Essentially if you have an "occurence", you're required to report it to NTSB, which in turn will grade it and decide if you need even a cursory interview.
https://www.law.cornell.edu/cfr/text/49/830.5
Also note: a landing that required repairs would not necessarily be an accident either, assuming no serious injuries occurred. "Engine failure or damage limited to an engine if only one engine fails or is damaged, bent fairings or cowling, dented skin, small punctured holes in the skin or fabric, ground damage to rotor or propeller blades, and damage to landing gear, wheels, tires, flaps, engine accessories, brakes, or wingtips are not considered “substantial damage” for the purpose of this part." (Those minor damages, even if they made the airplane require repairs prior to further flight, are not enough to make that landing an accident.)
Aircraft accident means an occurrence associated with the operation of an aircraft which takes place between the time any person boards the aircraft with the intention of flight and all such persons have disembarked, and in which any person suffers death or serious injury, or in which the aircraft receives substantial damage. "
https://www.law.cornell.edu/cfr/text/49/830.2
Later on the same page you can see how they define "substantial damage" and "civil aircraft" too.
Mind you, this is usually done for incidents, not accidents. However, sometimes an accident is clearly due to illegal operation, and sometimes that means that a) matter is passed directly to prosecution b) investigation is closed without conclusion due to explicit disregard of safety mechanisms, thus making further investigation useless to the purpose of aircraft accident investigation (under common rules from ICAO that NTSB also operates when it comes to aircraft)
The definition of an aircraft accident is a matter of federal law: https://www.law.cornell.edu/cfr/text/49/830.2
An aircraft crash where the aircraft suffers minor damage and no one is seriously injured is, by definition, not an aircraft accident, but rather an incident. (This incident is definitely an aircraft accident, of course, whether or not it was accidental. :) )
There is prior art for non-accidental plane crashes: https://www.youtube.com/watch?v=LhoxaJTzPu4
I believe the claims made by the GP are still clearly wrong, given that they do use the term "accident" and stipulate criteria for investigation that (commercial or passengers) that have no basis in the definition your provided or the NTSB's mandate.
Probably not (assuming you're trying to determine reporting requirements and figuring out if it's substantial damage). It's specifically excluded: "ground damage to rotor or propeller blades, and damage to landing gear, wheels, tires, flaps, engine accessories, brakes, or wingtips are not considered “substantial damage” for the purpose of this part." The NTSB doesn't want to be bothered everytime a prop makes ground contact, hits a runway light, a towbar, etc. It happens a lot.
The "investigation" consisted of the airport director speaking with the PIC and passenger (me.) His sole question to me was "were you operating the aircraft?"
There are a lot of stories of pretty terrible decisions made by GA pilots and little/nothing happening from the FAA. And then do stupid shit like going after Bob Hoover's license because he was too old for their tastes.