I remember he draw such diagram almost every lesson to explain the mathematical structure of various information theory topics.
Check out Lewis Carol's Logic Game:
But the Venn diagrams are presented in their book as mnemonic tools, and not in terms of entropies of an underlying "I-measure" as in the article. (Of course, the book is an introduction, not in a theorem/proof format.) So you're not sure how far the notions can be extended.
The world of information theory was small then, and the author of the paper would have been well-known to both Cover and Thomas.