I'm not the only one who has this view.
From Paul Graham, http://www.paulgraham.com/rootsoflisp.html
"There were already models of computation, of course - most notably the Turing Machine. But Turing Machine programs are not very edifying to read. If you want a language for describing algorithms, you might want something more abstract, and that was one of McCarthy's aims in defining Lisp. The language he defined in 1960 was missing a lot. It has no side-effects, no sequential execution (which is useful only with side effects anyway), no practical numbers, and dynamic scope. But these limitations can be remedied with surprisingly little additional code. If you understand McCarthy's eval you understand more than just a stage in the history of languages. These ideas are still the semantic core of Lisp today. So studying McCarthy's original paper shows us, in a sense, what Lisp really is. It' s not something that McCarthy designed so much as something he discovered. It's not intrinsically a language for AI or for rapid prototyping, or any other task at that level. It's what you get (or one thing you get) when you try to axiomatize computation."
Since the word LISP is not mathematically defined and has different meanings in different contexts, there are different views of what LISP is and I understand your confusion.