What can't happen is inter-generational transmission of particular subjective experiences that aren't paired with specific, unique metabolic, hormonal, and gene-expression signatures. Only biomolecular-mediated phenotypes, the most general and obvious of which would be things like stress or exercise or diet, make sense to be transmitted that way.
For instance, someone who's chronically afraid might transmit some kind of stress/fear modulating signals to offspring. 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. Therefore, I don't know why the article uses the term "lived experience", which is too broad a term to describe what the research suggests might be occurring.