Ha, indeed. I should have made the analogy with finding a linear change of variables such that the result is decomposable into a product of independent distributions -- ie if (x,y) is distributed on a narrow band about the unit circle in R^2 then there is no linear change of variables that renders this distribution independent, yet a (nonlinear) change to polar coordinates does give independence.

Perhaps the way to construct a counterexample to UDT is to try to create causal links between <your decision algorithm> and <the world> of the same nature as the links between <you> and the <world> in e.g. Newcomb's problem. I haven't thought this through any further.