This is neither how a Monte-Carlo process works (it's sampling the possible outcomes randomly, not simulating all outcomes), nor what is described here (building a physical system where an observable value is described by the differential equation one is trying to solve).
In practice the number of simulated scenarii is quite large which is what I meant by "every". Not rigorous though, I concur.
Monte Carlo methods are used to solve partial differential equations, I found both approaches similar in the sense that they look at how the system actually/could behave, instead of looking at the equations solely.
This is a pedantic response. There isn't an important difference between building a physical system and building a system in code whose generating process is that which you're trying to model. And everyone knew he didn't mean every outcome literally.
