If history teaches anything about dealing with these types of agencies, we should remember always a couple of points:
1. Agencies *NEVER* have to say a word, unless compelled by rulings of appropriate jurisdiction courts and
2. Those in "contest" with agencies can be irreparably harmed by saying the "wrong things" in public.
My point being, that I would most certainly wager that AMA counsel has said "Ya'll be VERY careful what you say - anyplace" and that the FAA's counsel has reminded them "You have jurisdiction and legal authority; you don't need to say anything to anyone".
I know these comments may be uncomfortable to read, but my experiences dealing with various legal entities related to FDA, Medicare, SSA, and the DHHS professionally over many, many years has taught me well.