Bell's Theorem does not prove that. It is a theorem itself, so this theorem has been proven using quantum theory and other assumptions in Bell's paper.
In the quote, notice "Bell tests...have consistently found" and the word local. So not the Theorem, but the "Bell test" experiments' results, when interpreted using theorems like the Bell theorem and similar, show nature manifests non-local behaviour. They do not prove your belief that hidden variables do not exist.
Also, I recommend using more reliables sources than Wikipedia to argue a point about physics. It is not a reliable source, even though it is useful for discovery and occasionaly is correct.
In the quote, notice "Bell tests...have consistently found" and the word local. So not the Theorem, but the "Bell test" experiments' results, when interpreted using theorems like the Bell theorem and similar, show nature manifests non-local behaviour. They do not prove your belief that hidden variables do not exist.
More details on this:
http://www.scholarpedia.org/article/Bell%27s_theorem#Missing...
Also, I recommend using more reliables sources than Wikipedia to argue a point about physics. It is not a reliable source, even though it is useful for discovery and occasionaly is correct.