A human might read that book and be unable to control how they react to that information (maybe you might look at your brother differently if you knew what he wrote).

In contrast, a computer could read the book, do a bunch of processing on it, run it through a few neural nets, check your brother's privacy settings, see that the book is marked as private, then erase all its "memories" of the book from existence; the result being absolutely no different from if it had never "read" the book at all.

So even if it were true that "Facebook will run face recognition on the photo regardless", that would be irrelevant as long as it does nothing with the information obtained via that algorithm. And if you don't trust Facebook to honor your privacy setting and do nothing with the information, you shouldn't trust them to not run the facial recognition algorithm in the first place.