Simulation proves only the theory - sampling and experimentation proves the implementation. Otherwise it might be entirely possible for the packaging process to fill an exact match at a far higher rate - and for the mix to NOT be random.

But the experiment also does not prove much beyond that it was 488 in this particular one case or does it?

He also has 488 samples of skittle distributions which can be used to validate the model assumptions on their own.

Or to make a lot of kids happy.

It would not have been practical to design a simulation of a Skittles packaging machine, as the design of those machines is not public information.

How would he know what distribution to use for the simulation without a sufficiently large dataset to use as an example? A simulation of a made-up system is pretty worthless.

But a simulation would not be able to prove your assumptions correct and would do nothing but validate your math.

All your math can be correct but if your assumptions are incorrect, your results may not be accurate.

But "fill bags with random colors" is already basing your simulation on the assumption that the colors are uniformly distributed. And in fact, that seems to be one of the things he found incorrect in his actual experiment.