I think you're viewing this too simplistically (although I'm about to walk down a mighty simple path myself).
Lets just imagine that we're using NN, and of course ML is large topic, not limited to NN, but this is sufficient for now. Adding new data points changes the weights on the neural network -- or can even add new inputs or hidden layers.
I don't actually know what the hot coals trick is, but lets say that it is walking over them at the right rate -- this info gets added to the inputs, with no burning as the output (of course its probably not a step function).
Basically you've now increased what you know... burning is a function of temperature and duration.
No change to the fundamental algorithm.
To be clear... adding a new data point doesn't just change how you react to that one piece of stimulus, but depending on what context is provided, it can change all the weights and structure of the NN. Effectively, change your world view.