> Someone who's afraid of a specific thing, however, cannot transmit fear of that specific thing unless there's some incredible and unexplored cognition-to-biomolecular signalling mechanism that's entirely unexplored and undescribed.

While there is absolutely no conclusive evidence, there are a few studies that indicate this is a possibility.

One such study from 2013: https://www.nature.com/articles/nn.3594

Again, there’s not strong proof- but at least plausible evidence.

It does depend on how specific the thing is. Spiders in general maybe, but for a particular type of spider seems to have close to nil possibility.