I'm late to this thread and haven't read through it yet, so I apologize if this issue has already been addressed.
If Cruz has reasonable grounds to believe he qualifies as a natural born citizen, there is no intent to commit fraud. No court in the land would convict someone under these circumstances.
The question of what constitutes a natural born citizen is clearly not as firmly established as some would want to believe. Cruz has lots of legal authorities who agree with his position.
he is a constitutional lawyer who has argued before the Supreme Court and to say he is not aware of Rogers v. Bellei (1971), a frequently referenced SCOTUS case used to this day, even by the government, if this be the case, the Cruz is no constitutional scholar and a very ill educated lawyer.