Turing test does not assume brain's a machine
If a machine were to pass the test, it wouldn't tell us anything about the relation between brains and machines. It would only show that some machines are capable of thinking, whether those machines are like brains or not.
The Moor Argument
"...the Turing Test in no way depends upon the assumption that the brain is a machine. My claim is that if the test was passed in the sense discussed above, then one should conclude that both men and machines can think. One is not forced to assume or conclude from this that brains are machines (or machines are brains) any more than one would assume or conclude that a human who printed very well must be a typewriter" (Moor, 1976, p. 253).
Source: Moor, James (1976) "An analysis of the Turing test." Philosophical Studies 30: 249-257.