Your last sentence nails it, deepest lore. In Mario Kart, the Kart is actually part of the player, the reaction to make the player larger requires antacids in the stomach to break down the mushroom thus releasing the magical properties to make Mario bigger.
In Mario Kart because the Kart is part of the player, the mushroom is fed to the Kart which means that the mushroom reacts along with the petrol as part of the combustion thus creating a small explosion which propels the character along at a slightly faster speed for a short period of time.