This, along with the conclusion, is wrong in the first example:

  N(μ=30×0.2,σ=30×0.9).

  With these parameters, 16 MB should have a z score of about 2, and my computer Using slightly more precise numbers. helpfully tells me it’s 2.38, which under the normal distribution corresponds to a probability of 0.8 %. 

  [...]

  The last point is the most important one for the question we set out with. The actual risk of the files not fitting is 6× higher than the central limit theorem would have us believe. 

The probability implied by the normal distribution is 2.1%, not 0.8%:

  > 1 - pnorm(16, 30 * 0.2, sqrt(30) * 0.9)
  [1] 0.02124942

So the actual probability of the files not fitting is only 2.26 times higher than implied probability. I think this is actually quite impressive. At n = 30, we are talking about a very small sample, one for which we don't usually use the central limit theorem.