So I wouldn't exactly call that entanglement, although I concede there is a subtle point there. I would instead say that it is a rather interesting statement about the form certain types of entanglement can take. Also, the anti-symmetrization of the wavefunction is really a consequence of the spin-statistics theorem, which crucially relies on the existence of local relativistic field theory.
Now I want to emphasize that this is not merely intuition, but rather the history of a long line of failed attempts. So, if someone thinks that they can write down a local theory that can 'create' entanglement at spacelike separation out of thin air, without using a local, and causal third party (like a messenger particle in the case of entanglement swapping), then write down that theory. The problem will become obvious the second you attempt to do that, as you will find that you need to write down an interaction Hamiltonian that will either involve fields that are evaluated at different spacetime points, or that will require higher derivatives. I think this is where the Bohmians run into issues. They have to be able to allow ftl communication between say EPR pairs, but not for anything else, which then requires imposition of extra rules that adds theoretical baggage. As I said, I don't really know how successful they are with that.