As I understand it the problem with the FAA is that they wear two conflicting hats, regulatory and promotion of industry, whereas the NTSB doesn't have _that_ issue?
As such I would hope that 1) the NTSB would be involved and 2) that their threshold for involvement would be low, e.g., malfunction.
There is an agreement between the two agencies to collaborate on commercial space investigation accidents of a certain level. The FAA does most of the work right now through their mishap investigations.