"We choose an arbitrary point in the sample space independent of the outcome of the experiment and call it the origin. Of course, in the way we have expressed the problem this choice has already been made, but in a correct coordinate-free presentation, it would appear as an arbitrary choice of one point in an affine space."

The James-Stein estimator in its general form is about shrinking towards an arbitrary point (which usually is not the origin). It respects translational symmetry if you transform that arbitrary point like everything else.