I bought this book because it gets so many good mentions. I was intrigued how anyone could write a whole book about such a basically simple subject. To be honest, I really don't rate it at all. I think it is confusing and almost deliberately complicates things in order to justify itself. However, I have to concede that a lot of people think it's great so I guess it must be doing something right.
You mention The Sky Brothers from the book. That's Brother Blue Sky, Brother Backlit Sky (aren't all skies backlit?), Brother Dusky Blue Sky and Brother Reflecting Sky. I don't find that helpful. What is he on about? It just sounds like fancy rhetoric.
He doesn't mention spot metering specifically, but then suggests you take a reading "to the side of the sun." From the illustrations, you can't do that without a spot meter so I guess that's your answer for whether you need one or not.
Exposure metering is like this. In every scene there is a wide range of tones from light to dark. In everyday photography, that range is several hundred to one, and in a sunset it can be thousands to one. Your camera sensor can only handle a range of about seven stops, maybe eight, and that is a ratio of 128 to one, or 256 max. That is the dynamic range, and there's the problem. You cannot change this, and you cannot magic up an extended dynamic range with any method of metering.
Fortunately, there is usually a fairly small range of tones within the whole scene that are important to the photograph, so the task is to make sure you get those important tones to fall within the range that the camera can handle. You must decide on what is important (ie what is it that your are trying to capture in the photo) and then adjust the exposure level to slide those particular tones up and down within the total scale so that they sit within the range that the camera can record.
You will almost always lose both some bright tones and extremely dark ones from the top and bottom of the scale, and if this is unacceptable then there are a few tricks you can use, such as a graduated filter, HDR technique, a polarising filter, perhaps flash etc which either reduces the bright tones, or boosts the darker ones, to move them within the camera's dynamic range.
This is what the exposure meter is helping you to do and while it does a pretty good job (matrix/evaluative metering is really smart these days) it is not infallible. With film, this was a real problem, but with digital you have a histogram. The histogram is an incredible invention, and it is far more helpful than ten books about exposure. So when in doubt, take a quick snap and
look at the histogram. It will tell you exactly the range of tones you have captured successfully and where they fall within the dynamic range. Also check the LCD image and if you have over exposure alert switched on (blinkies) it will flash at you.
Frankly, with these kinds of aids literally at your finger tips and available in an instant, it is surely not too hard to get optimum exposure under any situation. It might not always be what you would hope for, but at least it will be the best you can get. No amount of tricky metering techniques can make it any better than chimping the histogram and LCD image, and making simple adjustments so that it looks the best way it can.
HTH