I believe the opposite is true:
this chart, and others like it pander to and only convince the very naive who need to find an over-arching narrative with which they can explain the world. Little grains of truth are to be found in it and at particular points in time some of the hierarchies in it function as described. However, there is no narrative.
This chart describes a level of cooperation and competence that human organizations could never achieve.
It may be true that the B.I.S has more power than yu=ou would expect from such a small, obscure entity.
It may be true that central banks have a bit more influence than their technocratic mandates would suggest.
It certainly true that certain rich families or corporations (Rockefellers, Bill Gates, Big Oil, Big Pharma, Big Tech) have more lobbying power than what is good for society, though placing the Rockefellers above national governments smells of you-know-what.
But to believe that all these people and organizations put aside their particular vested interests and egos to join in this genius, massive, unprecedented, global and yet secret mechanism by which they control science, media, finance and politics the world over?
To believe in Darth Vader is as naive as believing in Santa.
Going back to Brexit, this theory of the world could anecdotally explain why Brexit happened, but had the vote gone the other way, it would find the anecdotes for that as well because nobody really knows what BIS does, hence what its motives are and why would you ruin a narrative in which you are thoughtful and knowledgable and others the ignorant sheep?