Since we're getting pedantic, as HN is wont to do, I'm not sure if the parent complaint is about the first sentence...
> VOLTAGE is to electricity what pressure is to water: the more you have of it the more oomph you get.
... or about the claim that follows:
> That is why electrical power lines work at high voltage.
The former sentence (aka the hydraulic analogy, [1]) is a very well-established thing. It's not a perfect analogy, but it's quite reasonable. The latter (high voltage power lines) is demonstrably not correct, as the two of you have pointed out.
Extending your power formula to the hydraulic world and simplifying the calculus to steady-state algebra:
Power = (Volumetric flow rate) * (pressure)
Though, to be fair, the analogy breaks down a little there; the Poiseuille equation [2] (the fluid equivalent of V = IR) involves 6 variables instead of 3. But the point is, you still end up with a final equation of similar form to P = (I^2)R.
[1] https://en.wikipedia.org/wiki/Hydraulic_analogy
[2] https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equat...