Is this true? Couldn't I put the mark on a page of my book and photocopiers would still detect and refuse to copy that page?

Yes, absolutely. It's a pattern of five rings, well-documented although Omron appears to keep the exact details pretty tightly held.

They don't have to be exact circles, they just have to be some dots in about the right place. In the UK, the Bank of England issued notes with Elgar on them and the EURion constellation picked out in musical notes ;-)