There is a great deal of difference between it operating, in certain regards, on the same sort of rules (rules isomorphic to) mathematics, and mathematics being applicable because physics isn't logically inconsistent. It's not a logical contradiction to say that two points have the same position, nor to say that 2+2=1 (for the latter, consider arithmetic modulo 3). Nor can maths be deduced purely from logic; partly because logic doesn't require the existence of more than one object.

Russell did try to deduce maths from logic plus some axioms about how the world worked - that there were an infinite number of things, etc., but the applicability of the maths is always going to be an empirical question.