I may be missing things.
The supernatural is always lurking around the corner as a possible explanation for very unusual events for us, no matter how skeptical we are. We dismiss that possibility very quickly, most of us, but if we saw something white and shimmering for a moment in a dark old house when a cold wind is coming through the window and creaking noises are going on, first thought, ghost. In fact I think they bend over backwards a little too far on supernatural shows to depict all (uninformed) characters as total skeptics.
In any group the size of the Collins family, someone will consider a story like Elizabeth's I think, at least if it appears to be coming true at least partly in front of their eyes, and even if no one mentioned the supernatural.
I'm not sure what else they could do, myself.... I'd expect them to start considering that her fear might have been genuine, though. I would have.