The Constitution does not prohibit a non-citizen or an ineligible citizen from running for POTUS. It only makes him ineligible to take the office.
I believe it is imperative that the SCOTUS ensure the constitutional eligibility of an elected candidate to take the office that the Chief Justice of the Supreme court is mandated to give the oath of office to.
If Roberts is going to swear this guy in, then Roberts has a constitutional obligation to make sure that he is eligible to take the office.
If Roberts doesn't do it, then he has violated HIS oath and he should be removed.