I think the FAA is stretching its mission statement with this investigation. Calling a development test result a "mishap" seems to imply that if you don't meet all of your mission goals on every try of a development project, there is something wrong with the project implementation. Of course, that is B.S. The FAA's legal responsibility is to ensure public safety, both from accidents that involve the public commercially, such as commercial aircraft crashes, and development projects that could hurt the public with flying debris or chemical contamination from aircraft that do not involve humans as passengers or crew.
I have no issue with the FAA looking into a perceived problem on the first flight with the Flight Termination System apparently not working as designed, because that could threaten the public if the system fails to destroy the rocket when it heads out of the planned trajectory.
But, explosions of rockets under development are anticipated events, which are planned to occur in a safe manner when they happen. So, unless the FAA has some reason to think that something violated the safety plan, rather than just failing to fulfill the fondest hopes of the developers, the FAA should not create any delays in the development process. I doubt that SpaceX needs any "help" from the FAA to figure out what went wrong and engineer solutions.