Being elected and being eligible are two different things. Being elected does not make you eligible to hold the office if you do not have proof of eligibility. He did not have proof nor to this day have we seen proof. Since the Twentieth Amendment, Section Three REQUIRES that Congress sees proof, he had to present it to them or he could not serve legally in the office of President. A fake birth certificate is not proof of eligibility but is closer to being proof that there is no birth certificate available.