Covalent character of hydrogen bonds

Originally, it was thought that hydrogen bonds were largely electrostatic. Consider the situation D-H..A (where D and A denote donor and acceptor atoms respectively). Then one can calculation the electrostatic potential associated with the charge density associated with a D- anion and the A atom and one finds a minimum somewhere near where the proton sits. However, it turns out (particularly for "short" D-A distances, i.e. strong bonds) that there can be significant covalent character to the D-H and H...A bonds. Three complementary ways to describe this are in terms of

1. a valence bond (VB) picture where there is a quantum superposition of D-H and H-A bonds (which are partially covalent and partially ionic)
2. a molecular orbital picture of 4 electrons in 3 orbitals
3. a donor-acceptor natural orbital picture

But is there any definitive experimental evidence for covalent character? Two are cited:

• Compton scattering from ice (I need to read the PRL and understand it) 
• J Coupling of the D and A nuclear spins observed via NMR (first observation described in this JACS paper).

For a physicist and non-expert on NMR it is hard to follow the latter. However, I suspect what is going on is the following.

Please correct me if I am wrong. 

There is a hyperfine coupling between the D nucleus (A nucleus) and an electron which is largely localised on the D atom (A atom). But this D electron forms a "bond" (i.e. its spin is partly entangled with) with another electron localised on the H atom. But this electron in the H atom orbital also forms a bond with the electron in the A orbital. The net effect is there is some entanglement (covalency) between the electrons in the D and A orbitals. This in turn leads to entanglement (i.e. a spin-spin interaction) between the D and A nuclear spins. 

In contrast, if everything was purely classical and electrostatic there would be no quantum mechanical phase coherence between electron spins associated with the D and A atoms.