Discussion on question by JonathanReez: What is the penalty for dual US citizens who lie on the ESTA form in order to enter under VWP using their second passport?

You know, the question tacitly assumes that it's necessary to lie to accomplish this, but do we actually know that? What actually happens if you fill out an ESTA application and state that you have US citizenship but no US passport? Does it automatically reject your application? In light of the note I mentioned above, it's possible that it doesn't.