The reviewer's point is this:
"Finally, the author is not asking me to personally give more money to the government, he wants me to support forcing other people to do it. But those other people have average luck, by definition "
But that's wrong; if the tax is progressive, and you take it as given that the successful are lucky, then you are in fact taxing the lucky with a progressive tax. The question is targeting the tax correctly.
Even in that statement you quoted out of context, the reviewer is referring to how we all have the same amount of luck, so luck alone shouldn't be the basis for a progressive tax.
Now, there are good reasons for a progressive tax, but the reviewer is saying it doesn't justify ignoring illogical arguments in the book. Just because the conclusion is proven right somewhere else doesn't mean that all arguments for it are valid.
You started to address the review but switched to ad hom attacks to discredit the reviewer - when in reality the reviewer is a past financial professor who works in risk management, and makes some very salient points about the logic behind the books claims.
Even what you say about sampling binomial vs. exponential populations isn't quite relevant, because as a coin or a person, you're not going to be switching between such distributions when sampling.