Two persistent misconceptions about hydrogen bonding?

Misconception 1?
         "H-bonding interactions are dominated by electrostatics"
This is stated in Assessment of the Performance of DFT and DFT-D Methods for Describing Distance Dependence of Hydrogen-Bonded Interactions, one of the most downloaded recent papers in Journal of Chemical Theory and Computation.
Earlier posts discuss the importance of covalent interactions, particularly in shorter (stronger) Hydrogen bonds.


Misconception 2?

“One of the most fundamental, yet enigmatic, of all chemical processes is the transfer of protons in liquid water, which occurs via ultrafast quantum tunneling in the hydrogen bonded network”.

This is stated in a 2003 Science article and challenged by Dominic Marx in Proton Transfer 200 Years after von Grotthuss: Insights from Ab Initio Simulations

proton transfer has often readily been explained by taking recourse to the appealing concept of “proton tunneling”,27–29 which was begotten shortly after the birth of quantum mechanics. It is essentially based on a static view derived from symmetrical one-dimensional double-well potentials V(δ), such as the one shown on the left in Figure 3 [see below], thus completely omitting the possibility of a barrierless scenario, as sketched in the central panel of this figure. 

For a discussion of the origin [in terms of covalent interactions!] of these three different potentials, see my preprint.