Since this is kind of a seperate issue, and yet not, I'm going to address it seperately because it really requires a rather thorough treatment:
It feels as though you're talking out both sides of your mouth. Or did you not notice I said time asymmetry?
I did notice. And don't blame me for talking about of both sides of my mouth, blame quantum field theory. That's the name of the game. But I'll try to do better here.
The problem (apart from the fact that I have probably explained things badly), is that
1) The terms in QFT with respect to time symmetry, transformations, and reversals don't even equate in general with the "similar" processes in classical mechanics, let alone the vernacular
2) The counter-intuitive nature of QFT itself makes it rather difficult to explain what is desired and why, and how the use of technical terms corresponds to
something a normal person might say
&
3) What is "desired" at a macroscopic scale (and even at times in the universe as a whole) and at the macroscopic local level are often different (or opposite) things
So I'm going to attempt a more complete explanation of the study you linked to, and the concepts in it, but in the wider context of modern physics (and the problems associated with it) in general.
I'm sure you know that even in classical mechanics, the "arrow of time" was a problem in two ways. First, classical physics required, for the most part (or at least implied) that time was symmetric. The idea is that for any given system, if you know all the laws and reverse them, you get what you started with. Time-symmetry is required for this. Yet we don't experience time symmetry, we only experience time going in one direction. So both time asymmetry and time symmetry are "problems", which were sort of resolved by thermodynamics in classical physics. Enter relativity and quantum theory, and a whole new way of dealing with these issues. Now, as long as we've thrown all reality as we know it out the window at the quantum level, why not throw in time-reversal too? If we can get microscopically local reversable systems, and do the same "vanishing h" act that we do with quantum nonlocality, we get two birds with one stones (and why not? after all, we have live and dead cats in two places at once).
But we need a new language for the new physics. Enter the CPT theorem which you are probably familiar with. Charge conjugation, spatial (parity) reflection, and time-reversal = CPT. Quantum field theory pretty much requires CPT invariance. In other words, at the quantum level, we need a system to be completely symmetric or reversable. It's fundamental to QFT, and unlike nonlocality (which nobody ever wanted), some manner of making localized systems symmetric which included time, but somehow explained why we experience time asymmetry, was just fantastic. How wonderful. Sure, there was an intial worry with the maximal violation of C and P, but with some nifty mathematics, we retained CP symmetry (and CPT invariance) and the world breathed a sigh of relief. Or rather, the small subset whom the rest of the world paid to deal with crap like this.
Your study is the latest in a series that began in 1964 which has yet to be resolved and is fundamentally problematic: CP violations themselves. But what has this to do with time?
Well, unlike the violations of C and P, the violation of CP together with the assumption of CPT invariance (again, that fundamental component of QFT), means a violation of time-reversal symmetry. To put it another way: assume that CPT invariance holds. If CP is violated, then given this assumption it can only be that we have a violation of CP
and T reversals. Under the assumption that reversing the system dynamics gets you the same system (that foundational component of QFT we call CPT invariance), we find that this violates CPT symmetry.
T-reversal is a bit misleading. And by a bit I mean totally. Because while it is "time-reversal" in some sense, it's really motion reversal. And as, in quantum mechanics, "motion" is such a difficult thing to deal with (so difficult, we don't deal with them, we ignore the actual system dynamics and make up something else we call the system), the idea of CPT invariance is about as fundamental as you can get in modern physics. Being able to, at the very least, take our mathematical systems and demonstrate how our "measurements" exhibit the desired symmetry brings us one step closer to explaining how the macroscopic world we experience derives from quantum reality.
As Bigi & Sanda put it in the opening of their book
CP Violation (
Cambridge Monographs on Particle Physics, Nuclear Physics, and Cosmology, vol. 28), the disparity between how we experience time and how it is described in physics could (we hoped), be "understood" if "microscopic T invariance" existed in such a way that the same invariance is "so unlikely to occur for a macroscopic system." However:
"It came as a great shock that microscopic T invariance is violated in nature, that ‘nature makes a difference between past and future’ even on the most fundamental level."
It is CP violations, along with the assumption of CPT invariance, which get us the time-reversal asymmetries we
don't want at the microscopic level, because we
needed these to explain how (like other quantum processes) something like "decoherence" made these vanish at the macroscopic level.
The study you linked to was "direct evidence" (relative to other evidence, anyway) of this reversal violation.
So on the one hand, it is a study which provides further evidence that quantum field theory's explanation for our uni-directional experience of time fails, and it does this through demonstrating that the means behind this explanation (microscopic symmetry which becomes unbelievably improbable at the macroscopic level), is violated.
It is another challenge for QFT theory, and another step back in deriving the "classical" world from the quantum "reality".
Also, you better take away Feynman's PhD if constructing classical physics from quantum has "no theorectical basis." 
