Here is the direct link to the article:
http://www.heritage.org/constitution/#!/articles/2/essays/90/treaty-clause
I don’t see anything about the Magna Carta in there.
My initial reason says the Senate must advise and consent at the 2/3rds level EXCEPT in executive agreements that are related to an already passed treaty. Congressional-Executive agreements bypass the Constitution, but the courts have upheld it since Congress acquiesced. The problem is that the 2/3rds rule was imposed to insure that a treaty was beneficial to the entire country and not to just to power bloc(s).
The overall thrust of the article seems to be indicating that the constitution isn’t being followed, but that has happened so often that Scotus now considers that to be the way things work. That is a mindset that needs to change.
I’m sure that Cruz, being a constitutional lawyer, operates on these understandings, so he deserves a bit of sympathy from us....but certainly not for agreeing to bad deals like Iran-Nuke and Obama Trade Power.