Reddit reviews Practical Aviation Law (eBook - epub)

Speaking as a former controller, hell no. That is 100% outside of what constitutes a binding control instruction.

Not to say I haven't done it myself, but as a pilot you don't have any obligation to potentially incriminate yourself.

For further reading, I recommend Hamilton's Practical Aviation Law. It's a pretty easy read and it contains basic legal information for all pilots.

FAA aren't the police and can't detain you. Fleeing the interview doesn't matter. They have your address from your license, so it's not like you'll be getting away from questioning, but you never want to talk with the FAA after an incident without a lawyer because nothing that you say is protected. If it interests you, you should read this:
http://www.amazon.com/Practical-Aviation-Law-Scott-Hamilton/dp/1560277637