This is now a semantic discussion - which is not necessarily a bad thing, we should just know that up front.
To me, the statement "programming without assignment" implies programming without making multiple assignments to the same name - mutation or re-assignment. I don't know if the programming language community has agreed-upon semantics for the word "assignment," but to me, it implies re-assignment and mutation. What you call "assignment" I think of as binding - that is, the lvalue gets bound to the rvalue.
The technical terms are 'variable assignment' and 'single assignment'. 'Assigment' is generally considered to mean the former unless it's qualified.
From a pedantic perspective, you can't really disagree with the statement 'haskell supports single assignment.' But equally as pedantic, most actual text reads 'FP doesn't support variable assignment', including the original article above.
I don't have a copy of the Ravi Sethi book to see what the exact text of his exact statement was.
To me, the statement "programming without assignment" implies programming without making multiple assignments to the same name - mutation or re-assignment. I don't know if the programming language community has agreed-upon semantics for the word "assignment," but to me, it implies re-assignment and mutation. What you call "assignment" I think of as binding - that is, the lvalue gets bound to the rvalue.