The darknet is a tiny subset of the "deep web," which includes anything that isn't publicly accessible. Examples would include bank accounts, settings pages on Facebook, etc. I'm fully ready to believe that the latter is much, much larger than everything else, but the author clearly has the two conflated.

I guess the way it's written it's technically true - if you count the darknet as part of the deepweb, then it is indeed in the deepweb that you find the nasty bits. But that's extremely disingenuous, and it seems more likely that the author doesn't understand it.