The short answer is Yes, NTSB and FAA do have the authority to request that you comply with federal law. Title 49 of the United States Code is where the NTSB and FAA get their authority from. I would highly recommend you get an attorney ASAP and comply with the requests. The NTSB investigates aircraft accidents to determine probable cause. The FAA investigates to determine if there were any non compliance with 14 CFR.

The company/owner of the aircraft is probably not very happy either.

Welcome to the world of LIABILITY in aviation....

If you were not acting or serving as the PIC or a Required Flight Crewmember, this will help as the PIC is ultimately responsible.

You probably should not provide further details on a public forum, but be prepared for an interview with questions like:

What type of Aircraft was it? Did it require two pilots? What was the "agreement" (verbal or written) between you and the company when you occupied the right seat? Was the operation Part 91 or 135? All of these questions will be asked...

Sorry to hear about this. I would not ignore these requests as things could get ugly and serious in short order. No Joke!