I would estimate this happens to about 75% of people who have/had anxiety.
Try and remember that anxiety doesn't always provide you with immediate feedback, and just because you don't 'feel' anxious right now, it doesn't mean your CNS isn't still reeling from what happened weeks/months before.
In my experience, your book is suggesting the right approach. You can't fight insomnia, you just have to learn to live with it until it passes. I also read a lot of information about dealing with insomnia and something that often worked for me was just getting up and walking around for 5 minutes, or getting a drink of water etc. Reading helps too.
Sounds like you're on the right path anyway