I'm going to disagree that 'how to think' should be an alternate title. 'Accidental Genius' is exactly what it is... You just pour out your thoughts like monkeys at typewriters, hoping to get something good. Now, since we're a little better at typing than monkeys, chances are that you'll happen across some nuggets. But this should never be confused with actual logic which can be used on command to get results consistently, rather than randomly.
For a fiction writer, the difference may be negligible. For a rocket scientist, it's a matter of life and death. Literally.
I think you are underestimating how much accidental thinking goes into the work of things like science. And providing a little bit of a strawman. I don't think the author of the book nor the reviewer intends this to replace "logical thinking" rather to support it for some people.
Sure there is a lot of logical thinking involved but some of the real insights where not based on the logical progression of thought in fact they where based on breaking them. Exactly to deliver insights outside the realm of the logical axioms.
You're talking about the creative aspect of science. For that aspect, this method may very well work. However, for turning that idea into an actual process or product, it won't work well at all.
Randomness is not as valuable as logic when working towards a specific end. That is, if you already know the beginning and the end, using randomness to find the path between them is probably the slowest and least likely to bring results.
It's not randomness it's "your thoughts on paper". That's not random, that starting with you.
I am not sure why you think logic is so central here. Of course you need logic, but it will only work if your premise is correct and IMHO if you are trying to solve a problem then most of the time it's your premise that's wrong not the logical reasoning that springs from it.
This is kind of interesting. Where does your thoughts come from? If I asked you to think of a famous person, and say the first person that comes to your mind, what determines whom you will think of? Presumably you were not thinking of a person before I asked. Did you have any choice in what person you started thinking about?
For a fiction writer, the difference may be negligible. For a rocket scientist, it's a matter of life and death. Literally.