The Twentieth Amendment, Section Three places the burden of proving eligibility squarely on the President Elect. If he/she fails to qualify, Congress must name an interim President. That Congress failed to do it’s job twice with Obama did not mean that Obama became a legal President, only that Congress allowed a usurpation of the office of President. That they did not enforce the Twentieth Amendment, Section Three on Obama does not mean that they will not enforce it on Cruz.
So, how does Cruz not qualify?
In your mind, what must he do to qualify?