The question the OP asked was "Does Dr. Gas have to report to the NPDB?"
Pretty sure that nobody has a duty to self report to NPDB. Your Med Staff office, employer or insurance company is supposed to take care of that😱 . Just one more reason that one should answer the question "if you have ever been involved in a malpractice action?" truthfully. You are supposed to be notified if there is an NPDB entry from anyone. One can always do a self query to see if there was an entry from a closed case.
FYI, 20+ years ago when we were a private group we wanted to deal with some Dental injuries ourselves...bad technique from a CRNA, student or doc. We were advised that if the group wrote a corporate check to the patient we had a duty to report. Same if our insurance carrier wrote the check, they had a duty to report. If the doc wrote a personal check...No duty to self report. That was the advice of our lawyer at the time. Not sure if accurate now or then, but that is what they told us.