In the soft-wet environment of biomolecular electron transfer, it is possible that structural fluctuations could wash out medium-specific electronic effects on electron tunneling rates. We show that beyond a transition distance (2-3 A in water and 6-7 A in proteins), fluctuation contributions to the mean-squared donor-to-acceptor tunneling matrix element are likely to dominate over the average matrix element. Even though fluctuations dominate the tunneling mechanism at larger distances, we find that the protein fold is "remembered" by the electronic coupling, and structure remains a key determinant of electron transfer kinetics.