Unfortunately, the SCOTUS has in fact amended the Constitution by its decisions quite a number of times during the past 100 years without explicitly stating so. The net result has been an ever growing and powerful government and ever diminishing civil liberties for the private citzen and the private sector.
Yes, like the eminent domain law. They might do it again should Obama not be eligible. No courage to go against the voters, even though it would have been OBAMA duping the voters, not the SCOTUS, if he was ineligible. He cannot claim he did not know he wasn't eligible, because of his obfuscations to this day.