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Does the Hodgkin-Huxley Model take into account the action of the ion pumps (e.g., Na-K-ATPase)?
The concentration differences do not vanish! An action potential requires extremely small ion fluxes, and thus the concentrations of sodium and potassium ions are mostly unaffected. In very small cells, with continuous activity, the internal concentration of ions can shift slightly. This is not a factor in the HH experiment, where the volumes both internally and externally are large and an infinite reservoir of ions is a reasonable approximation.
What makes people easily subscribe to pseudoscientific theories?
I really like this answer, but this discussion about whether predictions are essential to science is sort of puzzling. I think the term prediction is just being used in different ways. We can agree, I think, that a valid scientific statement or theory requires a testable hypothesis (at least in principle), which I would call a prediction. If it does not then it can no longer be called a scientific statement. Most experiments are a form of inductive reasoning about such predictions -- if A then B. B is true, so A is more plausible. Or, just as importantly, B is false, so A is less plausible.