I am sure you are just paraphrasing it incorrectly or left out the reference to expiration breakeven. Find the info and re read, it is the best way to learn the right way. You are asking the right questions so keep up the study as you will move up the learning curve easier with this kind of effort. best of luck.
You are right in your quote-- not just in one book but in plenty (of course not all books make that "mistake"). In addition, there might be a sentence there that would put the author off the hook, but the job of the book is not to hedge itself but to make sure that it loads your mind with the right understanding (and only the right understanding) that can make you money. You have a critical mind. With that attitude your odds to make money will increase substantially over time. Excellent start!
It is only true when there is no more time value in the option. Have a look at the formula of how the option price is calculated and look at its ingredients.