Without repeating myself too much, we are pretty sure that memory, as humans record it, is an exothermic chemical process. We cannot know what it is impossible for us to remember. That does not mean it isn't real, but we are not going to be aware of it. And reversal of time would be impossible to remember.
The thermodynamic arrow of time assumes physics is arranged in such a way that time never reverses. I do not think we can ascribe truth or falsehood to that, because we are dependent upon the idea of irreversible time to so high a degree that we seem unable to frame experiments that would test the idea. I think that we can imagine multiple dimensions of time, or even a rather complex topology imposed upon unidirectional time, but not a form of time that is singular but freely reverses. To the degree we can imagine reversible time as a version of multidimensional time, it would appear to be indistinguishable from raw indeterminacy, which we already observe, and to which we ascribe different causes.
I don't trust Popper's notion of falsifiability as a definition of science, but it is a wise position to obey if you are trying to think scientifically: It is inappropriate to make decisions about the truth of something, if you cannot imagine a result that would contradict your assumptions. And I would assert that we are biologically incapable of that particular feat of imagination.
So, I would go for this position being something very much like a tautology: It is necessarily and untestably true dictated not by deductive logic or definition, but instead by other basic structures of human thinking.