The physics of tides is largely well-understood, and the moon and sun provide the primary forcing. Accurate tide tables are regularly computed the world over, with measurements regularly made. Without even looking at measurements, the shipping industry demands accurate tide forecasts for navigating efficiently. The claim that "tidal phenomena are... primarily electromagnetic" requires some serious evidence to back it up, with calculates to boot, rather than invoking mysticism that tides are "beyond us". Many things are beyond our current scientific understanding, and that is humbling, but tides are quite well understood.
I don't have the scientific knowledge to assess all this. I'm not even sure how to understand properly the questions Jeanne Rousseau asks saying newtonian physics can't answer. What I hear however are competent people observing small variation in the properties of water and living systems that seems to be related to cosmic phenomenon, including moon phases. Variations we can also find in the atmosphere/ionosphere with more recent measurements of their ionic polarities. Adding to that are all the new discoveries that link weather phenomenon to electromagnetic influences from the sun, with water significantly influencing the electromagnetic properties of the atmosphere. Finally more people question the true molecular structure of water, as H2O seems to be a crude simplification over a dynamic mixture of isotopes and ions.
Overall the tidal theory is not a done deal, we only have approximate models, and this topic can be discussed for years to come. That's probably why she was told the tides is a phenomenon that is beyond us.