Yes, the structure of interactions is an essential issue to discriminate DL with HBM. DL seems to be a Brute force method, which needs more data and computational resource, while it may provide more general solutions. HBM need more human interaction in the structure learning process, so an accompanying advantage is that the resulting model is more interpretable as its structure is always under control through a given prior.
The compound idea of integrating DL with HBM seems natural, as I've also thought of it before. Anyway, the papers desearves a reading.