I mainly agree with your point. However, if it results in an off airport landing many times it is reported to the FAA/NTSB.
There are formal criteria of what it takes to be reported as an accident. And a landing on 'county road 18' with a trip to the airport on a rollback doesn't fulfill those criteria.
§830.2 Definitions.
As used in this part the following words or phrases are defined as follows:
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. For purposes of this part, the definition of “aircraft accident” includes “unmanned aircraft accident,” as defined herein.
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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.