It depends on where you pinch. If you start pinching everywhere, it is going to be very painful!
I am described by some as penny pincher. I am actually not; I just don't like to shop because it is stressful for me. So I try to avoid or delay as much as possible buying anything.
Now, having said that, there are downsides of blanket penny pinching. Instead of helping, it can be counter productive.
You mentioned the rich do not penny pinch as per the book's author. Well, rich spend money only if they can get a return from it; otherwise they will save(read invest) money as much as possible e.g. say if they want to buy a car, first they will see to it if they can pass it as business expense. Other reason they spend money is to project strength/status or for PR purpose. Another reason is for investment purpose, e.g. old paintings, wine, wintage cars, properties etc. So anything that they spend is used in a way to get back more money. Even if they spend on private jet, it is not just to project their status, it is to save them time to reach their destination and hence save money.
I was attending a course on entrepreneurship and the lecturer there once said that most successful entrepreneurs who do not own their own private jet travel by economy class.
Interestingly, I saw sometime back a teleseries on life of Paul Getty. In one of the scenes it is shown that he is recording in his pocket book the money spent on newspaper, and asks his butler to inform the owners of the newspaper that if the newspaper keeps on raising prices without improving the content then he will stop buying the paper :)