The discrepancy is probably explainable by game theory. There is some set of strategies, defined by the distribution you use to place your own ships and the distribution for picking guesses at enemy positions. If we start from the naive assumption of a uniform distribution for both, this strategy is exploitable using exactly the heatmap from the article. So next we can iterate, assume that the opposing player is using the heatmap from the article, and generate a new distribution of ship placements designed to be unlikely to be picked. From there we get a new heatmap, which can be iterated again in the same manner until eventual reaching convergence with the Nash Eq. I wonder what the Nash Eq of Battleship is and how similar it is to observed real player strategies.
For placement, I am fairly confident the best possible strategy will be one in which every tile has a uniform chance of being chosen for a ship. Any other strategy will result in the opponent being able to gain an advantage by preferring certain tiles when firing, and thus the equilibrium and best strategy will be one where that cannot happen.
However, I am also fairly certain that human players, especially those playing a casual iMessage battleships game, do a very bad job of following this strategy.
To be nitpicky, the process you described won't necessarily reach a Nash, as it may cycle. But if each player best-responds against the average of all opponent strategies so far, then said average strategies will converge to a Nash (fictitious play).
