A correct statement would be: "Given a solution set containing both the shortest path through fire and the shortest path avoiding fire, select the solution that fits within six tiles of movement, preferring the solution that avoids fire where possible."
It's a constraint optimization problem in disguise: generate a solution set, then filter and rank the set to return a canonical result. That describes most of the interesting problems in gameplay code: collision and physics can use that framing, and so can most things called "AI". They just all have been optimized to the point of obscuring the general case, so when a gamedev first encounters each they seem like unrelated things.
The specific reason why it seems confusing in this case is because while pathfinding algorithms are also a form of constraint optimization, they address the problem with iterative node exploration rather than brute forcing all solutions. And you can, if you are really enterprising, devise a way of beefing up A* to first explore one solution, then backtracking to try the other. And it might be a bit faster, but you are really working for the paycheck that day when the obvious thing is to run the basic A* algorithm twice with different configuration steps. You explore some redundant nodes, but you do it with less code.
