NTSB Party System
The only thing that matters is that the members bring expertise to the investigation and contribute (ask pertinent questions and answer questions).
The other world investigative agencies also seek the same level of participation in that regard by interested parties. Beyond that there are no doubt differences in operandi.
The thing that most prevents "any interested party" to the investigation is the immediate availability of quailfied investigators following an accident. Simply having an interest is not qualifications and after all there is only so much room for multiple experts in the field.
I was aware that external interest on TWA800, as an example, was handled in a reasonbly timely fashion by petitioning through the Washington NTSB Headquarters