Yes, the idea is that the particles themselves are connected to each other like two ends of a wormhole, so the signal about applied measurement doesn't have to take the 3km long path outside, but can directly go from one entangled particle to the other.

If this were the case we would expect to be able to send information through entangled particles. But it's well known that it cannot be used that way.

Entanglement would allow to send information if it was possible to clone quantum states https://en.wikipedia.org/wiki/No-communication_theorem#Some_.... If we are looking for a hidden variable theory, we need an explanation for no-cloning theorem independently from entanglement issue, so this does not add any additional restriction.