What has "proving" got to do with anything? It doesn't matter what you can prove, people want to believe what they want to believe.
Only a court can interpret the Constitution and the laws of the U.S. and they are not going to touch this one.
Anyone can "interpret" the Constitution. Only what the Court says is going to get enforced. This does not make the Court correct, it just means they have power.
I believe in an objective "right", and it remains correct even if people in authority don't agree. An example is this theory of legalized abortion. The Court said in Roe v Wade that the penumbra of the 14th amendment makes abortion legal.
I say the court is full of sh*t. They are wrong, but because they have power, their claim is enforced. Still wrong, but enforced none the less.
It sucks sometimes to have to follow the rule of law.