They’re not wrong: the mathematical definition of computation has gone effectively unchallenged since the publication of the Church-Turing Thesis in 1952, which claims that a function is computable (in the general philosophical sense) if, and only if, it is computable on a Turing Machine (and some other equivalent mathematical models). Our concern is with the physical world: what makes one physical object a computer, and another not? No physical computer can have an infinite amount of memory, so no physical computer can implement a TM in a simple literal way.