It’s more than that. People who have had heart transplants can inherit memories and personality traits from the donor. Cells remember more than they let on and can pass these memories to the recipient.

See this study. I think it’s safe to say we have some empirical evidence for this. In the linked study, there’s a kid who received a heart from another kid who died trying to retrieve a power ranger and somehow the donor knew that without anyone telling him. Another kid received a heart from a kid who drowned and he became afraid of water.