I don’t believe the above was Turings opinion for one moment. he absolutely knew that the math description of quantum mechanics was a generalization, and could be trivially specialized to discrete math (i.e. group and graph theory). Indeed, Id go so far as to say that the very notion of Turing reducibility is little more than one of knowing that a problem in the projected plane (of lesser info) can rely on the action of a subroutine in its non-projected space (of more info). Or, the n eigenfunctions of a multi-dimensional structure have something to offer solutions in equations restricted to the n-1 (only) eigenfunctions. Or, one can project (in lesser 3 dimension) from 4-term function space to the conjugate 4-term space.
He knows full well that quantum mechanics model ( in its probabalistic interpretation) is only a description (like in computable numbers) and thus has all the same properties of any other universal construct.
As Monty Python said: its just a model.