There is no law that requires the Chief Justice of the US to swear the president into office. It is tradition. If Roberts thought Obama was not eligible to serve as President, then he would have refused to perform the swearing in of Obama. That act alone would have brought the issue to an immediate head. Yes we have a system of laws in our country, and the Chief Justice of the USA is well aware of the law and the Constitution. It is obvious that he had zero questions regarding the eligibility of Obama. Don't forget that Roberts was described as “one of the foremost Constitutional scholar in our country” by Sen. Jeff Sessions at Roberts’ confirmation hearing. So yes, if Roberts felt Obama was not constitutionally eligible, could have refused to swear Obama into office.
You are the one who seems very prone to posting before engaging your brain.