I think the typical argument goes something along the lines of, "it uses []{} and doesn't make cons the default data structure, abandoning some simplicity-of-language."

It's not Lisp-as-in-Common-Lisp. It's closer to Scheme than to CL.

But it's "a Lisp" in the colloquial sense that it uses s-expression syntax and has macros.

Lisp: "List processing". Clojure doesn't even have cons cells... A Lisp without cons cells is like a C derivative without pointers...is it really C at that point? I'd also question the "profound belief that recursion is more intuitive than loops" since Lisp supports loops extremely well -- better than most languages, since you can build up your own iterative constructs using tagbody. And Clojure doesn't even have proper tail calls, so I doubt that Clojure actually believes in recursion.