> Why is this less likely than the alternative?
Because the alternative is quantum mechanics. If unconnected states can communicate, QM is wrong. QM is extremely unlikely to be wrong.
Caveat, ignorant answer coming: what I understand is as follows: we know that entangled quantum states can "communicate" through space-time (what Einstein called "spooky action at distance"). The paper therefore proves that either unconnected (not entangled) quantum states can communicate, or the wave function is real. They proceed to conclude that the first member of the alternative is less likely (justifiably I suppose).
It reminded me of the single electron universe hypothesis by Wheeler(http://en.wikipedia.org/wiki/One-electron_universe) and wonder if anyone can speak to whether this changes perception on seriousness/testability of that idea.