Why can a passing fire help some hard-coated seeds sprout?

Answer: Heat weakens the coat

Ash supplies nutrients — Ash can enrich the soil after a burn, so this is close to the right setting. But nutrients do not by themselves open a dormant hard-coated seed; the first problem is getting water and oxygen through the coat.

Heat weakens the coat ✓ — Heat can scar or weaken a hard seed coat, letting water and oxygen reach the embryo and restart growth. Fire also clears competing plants, so the seed is more likely to sprout when light and space are available.

Flames warm the embryo — The flame is not gently incubating the baby plant. Direct heat can kill an embryo if it is too intense; in fire-adapted seeds, the useful effect is usually a brief heat pulse that changes the protective coat, not warming the embryo like an egg.