Applying the test that you do (for finding Ted Cruz to be a natural Born Citizen of the United States), I don't find Cruz's father's immigration status to be relevant or material.
Just saying, you can dispense with this condition of qualifying for citizenship at birth. The relevant statute assigns citizenship regardless of the "other" parent's immigration status, provided the citizen parent meets the US residency conditions prescribed in the statute.
I understand, but some people still want to know about him.