Iron exposed to oxygen "burns", that's just chemistry, water increases the rate it will burn, but burn it will with or without water.
So Rust is a combustion reaction same as fire, and it produces the same heat as a fire but it is spread out over time so you won't be cooking any marsh mellows over that frame
This is why cutting off the oxygen contact is best, you cover a fire to put it out(cut off the oxygen), so painted or coated iron has less contact with oxygen and.....less "burning".
Your hole in the frame is a "hot spot", and like a grass fire "hot spot" it needs to be cooled or it will "burn" faster, more surface area.
It was probably at a spot where the factory paint/coating wore out, and a place that was wet some of the time.
Cooling the "flame", phosphoric acid converts reddish-brown iron(III) oxide, Fe2O3 (rust) to black ferric phosphate, FePO4, that's the chemistry part.
Coke and most similar soft drinks have phosphoric acid in them, it adds a tangy taste, but it's in pretty low amounts, but this is why people use Coke on rusty chrome, the phosphoric acid.
"Naval" jelly, was/is used by the US Navy to treat rust spots on the iron ships, which is where it got it's name, it is phosphoric acid in a gel form so it will stick to surfaces that may not be lying flat.
Best method is to clean surfaces with wire brush then apply the phosphoric acid/gel with a paint brush, I usually brush it again after 5 minutes, just moving around gel that's there, then rise it off with water after 10 minutes, then wire brush again and repeat.
After final rinse I let it dry, then paint the area.
You should do this and also have that spot reenforced/welded.
Wear rubber gloves and glasses when using phosphoric acid, also have some baking soda handy to neutralize the acid, just in case.
Phosphoric acid will ruin paint so be careful.
Some people use phosphoric acid and say it doesn't work, well chemistry is chemistry, so either they are not dealing with rust or the method used was flawed.