You’re not under oath when answering the question, unless there is a “I declare all this to be true under penalty of perjury” signature line you’re fine. You can also caveat that line with a comment to the effect that all rights are reserved and that it isn’t binding on any contracts.
Just thinking of Martha Stewart and Scooter Libby who got in trouble for lying to Fed Investigators.
How much of a stretch for the health care info gatherers to be labeled Fed Investigators?
Doesn’t feel like paranoia when they really are after me.