Was Brian Cox Wrong?

Recently, I watched Brian Cox, a well known physicist, on a TV lecture called Night With the Stars.  Here's a link to it: https://www.youtube.com/watch?v=5TQ28aA9gGo.  

The lecture was quite fascinating, as Brian is well known for making physics available to all.  But, Brian might have stepped too far by oversimplifying one of the greatest achievements in physics history: Pauli Exclusion Principle.

The Pauli Exclusion Principle basically says that every fermion (particles with half integer spins) has 4 quantum numbers, numbers that describe it, and no two electrons can share the same 4 numbers.  The numbers are quantum "spin" (not actually the spin of the fermion, no one knows what quantum spin looks like), energy level, azimuthal quantum number, and the magnetic quantum number (in simple terms, describing its magnetic properties.)

In the presentation, Brian Cox basically ignored all of the quantum numbers except for energy levels (formally known as principal quantum number) and made it seem as if everything was connected as mentioned in some religious philosophies.  After the presentation, many people started talking about how quantum mechanics "supports" the idea that everything is spiritually connected and we are connected with god.

Many physicists accuse Brian of messing up the meaning of quantum mechanics by oversimplifying it and allowing scientific spiritualists to make absurd comments.  Brian published an article to cover up his blunder and to explain how uncertainty due to the observer effect and the uncertainty principle (also very often confused, I'll make a post about that one too) make it impossible for a "spiritual connection".

Was Brian Cox wrong in simplifying Pauli Exclusion Principle?  In my opinion, he isn't because he just was trying to make it easier for non-physicists to understand and appreciate.  Imagine him trying to explain quantum spin when we don't even know what it is!  Sure he had a few technical errors but he shouldn't be criticized as much as he is.