Yes, but entropy means that the universe is not symmetric with respect to time, doesn't it? That is, enqk's statement is in fact a refutation of smilliken's claim. Dismissing it with "Congrats, you've discovered entropy" doesn't answer it at all.
Entropy is not due to the equations of our universe, but rather the initial conditions. So the asymmetry might be apparent but the equations might still be symmetric. Related is the idea of spontaneous symmetry breaking.
Of course, we don't have time symmetry in the equations anyway because of the weak force. But because the weak force is weak//doesn't matter much for the physics of many systems, we can often write the equations of physics as a time-symmetric term which essentially decides the motion plus a very small time-asymmetric term. So we can deal with the small term using techniques like perturbation theory, and use time symmetry for the rest.
> Of course, we don't have time symmetry in the equations anyway because of the weak force.
Could you expand on what you mean here? I've expected for a while that there was going to be something non-time-reversal-symmetric with the weak force, on the basis of parity violation (space-reversal doesn't give you the same equations) plus relativity (space and time are the same thing, at least kind of). But getting there directly from parity violation might require a faster-than-light frame of reference to observe it from, which is... let's just say it's experimentally difficult.
The answer, as you point out, is that CP violation implies T violation. Experimentally testing T violation is much, much harder, and I don't think has really been done in many systems (look at Fitch and Cronin's work for an example), but we know CP violation implies it. So it's there. Or at least, to our best knowledge, it's there -- T violation is not very well understood.
