My car is registered in California. If I drive to Mexico and have a traffic accident, should the California Highway Patrol get involved?
I suppose that would depend if you trust the Mexican Highway Patrol to bet to the bottom of it. /s
NTSB gets involved to determine if there are factors which might affect other aircraft of the same type.
IOW, the next time you charter a Lear 25, would you not appreciate knowing if the wing had fallen off THIS Lear 25?