What is the scientific basis for this last statement? Is it a consequence of GR, QM, both or some other theory? How would a layman gain some insight as to how this is possible?
That's a question that deserves a careful answer.
The laws of physics as they are currently understood are invariant under the symmetry t->-t. In words, they are identical going back in time as going forward in time.
* To understand the implications of that, let's first consider a more familiar example.
The laws of physics as they are currently understood are also invariant under rotations. And yet, when you look around you, you see that the room you're in is plainly not invariant under rotations (unless you happen to be sitting inside a perfect sphere). Neither is the solar system, neither is the galaxy, neither is the universe on the largest scales we can see (although it is close).
In fact, if the world were invariant under rotations, it would be extremely boring - because it would be perfectly spherical, with at most a dependence on radius from a single central point. But the laws of physics are also invariant under spatial translations - which would mean a totally symmetric world could even depend on that radius, but must be perfectly uniform and homogeneous. And since the laws of physics are also invariant under time translations, it could not depend on time either.
It turns out (perhaps it's obvious) that the only configuration that's invariant under all the symmetries of the laws of physics is a state that's completely empty of everything, one that's absolutely featureless and static. That state is known as the "vacuum". The reason we don't live in such a perfectly symmetrical state is, well, because it's completely empty.
So what good are these symmetries if they don't describe the world we actually do live in? The answer is that they tell us something very powerful. They tell us that starting from any solution, symmetric or not - for example, the world in the region around us - one can act on that solution with a symmetry (e.g. rotate it) and the result is
also a solution. That is to say: since we have proof that our part of the universe is a possible world, we can therefore conclude that a rotated version of it is also a possible world, and might exist somewhere. Somewhere far away might be another copy of the earth and the solar system, but rotated by 90 degrees. Note that I'm not saying it's likely or unlikely, just that it's guaranteed by the laws of physics to be possible and consistent. Symmetries transform solutions into other solutions, that's their power.
So: as I said at the beginning, one such symmetry is time-reversal, flipping past and future. Our part of the universe is not symmetric under that, since its past differs from its future. But that means that a region of the universe similar or identical to ours,
but running backwards in time, must also be a possible world, must also be a solution - and therefore might exist somewhere far away (and again I'm not saying it
does, just that it
might).
*Strictly speaking the symmetry is not t->-t, it also involves charge conjugation C and parity P (the full, true symmetry is called CPT) - but C and P are not relevant for this post, so I will ignore them.