Generally the dedication has its own pages that are not marked like the book pages, and generally 1/2 starts on its own sheet anyways.
There are exceptions, but almost every book I have used have followed the same pattern.
Your answer was indeed correct, the only time page 165/166 cannot be on the same page, is when the book has leading (unnumbered) pages, and in this case you could make the argument that the detective meant the 165th face of paper, irrelevant of markings by author.