Why not?
The "arrow of time" almost always requires thermodynamic arguments. And that requires a concentration of "low entropy" to move toward "high entropy". Which, by definition, are "boundary conditions" and not a fundamental part of your physical rules.
If, for example, your universe is entropically uniform, is there an "arrow of time"? And, even if there were, could you detect it?
However, I would like to point out that it's not like we haven't had this kind of issue before. The Bohr-Einstein debates were a good example. Einstein favored a "fields" interpretation of quantum mechanics. Unfortunately, Einstein's interpretation predicted that atomic states wouldn't decay, and that was clearly, obviously wrong, and Bohr very much hammered on that.
Except that Einstein wasn't "clearly, obviously wrong." As you increasingly isolate excited atoms, their atomic states take longer and longer to decay. The problem was that the experiments of the day couldn't create these kinds of singular quantum state systems--they were stuck with systems that were contaminated with lots of thermodynamic interactions.
We may be seeing something similar here. We are just starting to be able to put together the experiments that can probe things like Bell's Inequality. As we isolate these systems, we may find that the systems were contaminated with statistical time and that we get different results when we can isolate them.