I learned it's not 2.45 GHz. But what is it, then? In my failure to find the real value, I'm starting to wonder: does it even make sense talking about a resonant frequency of water molecules?
It depends on what you mean by resonate.
Water has three different vibrational modes - there are vibrational frequencies associated with these, but these are not really oscillations like a mass on a spring which we would be familiar with seeing. The webpage you link has some 'vibrational frequencies' of different molcules and notes they are significantly higher than the 2.45 GHz microwave range.
So water can be excited rotationally by 2.45 GHz - the rotational behaviour of water as single molecules in the gas phase is very complicated. Water is an 'asymmetric rotor', which turns out to be the hardest to understand. In liquid water the rotation is further complicated by collisions between adjacent molecules.
2.45 GHz is used is because it is a standard frequency that is allowed and doesn't interfere with licensed communications systems, part of the 2.4 GHz ISM band.
A lot of questions and answers here raise more ambiguity without addressing the fundamental underlying principle of the microwave-water interaction. A microwave heats (imparts kinetic energy) to water not through resonance (that would be an absurd preposition given water has ridiculously high mechanical resonance frequency) but rather from dipole interaction.
Water being a polar molecule gets activated by effect of its dipole moment (of about 2d) in a microwave field. The resulting molecules spin, being translated rotationally.
To answer your question: no, it doesn't make sense talking about a resonant frequency of water at the molecular level. At those levels, sound or other forms of classical excitation cannot achieve sustained resonance given the vast normal modes and DOF of liquid molecules.
Liquid water absorbs microwaves over a very broad frequency range. In the liquid many effects contribute to this broadening. Here you can find the microwave absorption of liquid water. The frequency maximum of the absorptivity ranges from 180 GHz at 0C to 9-10 GHz at 100C. So why pick 2.45 GHz for microwave ovens? This is to ensure a sufficiently large penetration depth. Food and drinks should be heated up throughout. At frequencies too close the absorption maximum the surface would be heated up much more than the bulk. Balancing this with efficiency requirements gives the much lower frequency of 2.45 GHz.
Water molecule resonates at different frequencies according to its vibrational and rotational modes. Those modes have quantum origin since classical rotational motion has no discrete transitions between different modes. These resonance frequencies altogether are used as a stamp proof of water molecules in infrared spectroscopy. The frequency 2.45 GHz corresponds to one of liquid water molecules' rotational mode transition energies.
For more information, I find Wikipedia article very instructive. To understand all the phenomenon, try to learn about resonance, rotational modes, absorption spectrum and dielectric loss.
What is important in the idea of resonance with water is to establish a frequency of excitation that causes the natural frequencies to superimpose or wave superposition. By achieving wave superposition the amplitude of the oscillations will have the greatest potential of breaking the molecule into its elemental constituents thereby creating free atoms that can recombine to form the diatomic molecules desired. H2 and O2 Oddly enough chemistry and properties of elements can play into this process as the electrodes used if they are constructed of platinum will result in a better yield from hydrolysis. This may be the result of how the atomic structure of platinum releases electrons through solution. A similar process has been observed in certain solar cells as alloys of atoms are placed on layers of silicon substrate creating a resonant cavity to enhance voltage production through the capture of photons. The explanation comes from the energy level of exchange of electrons during enthalpy processes that exceed the enthalpy energy required to break the covalent bonds of H2O.