I think you're missing something. BitTorrent implements the solution you describe.
You as the author create the (small) .torrent file with the checksums in it. You host this on your webserver and link to it. The first step of a BitTorrent session is for the user to download these checksums directly from you.
Then BitTorrent does its peer to peer magic and retrieves the actual file (your pdf). The client checks the pdf against the .torrent file to ensure that what the user gets is exactly what you created.
If you still disagree, please read about the BitTorrent protocol. It's a very different beast than the Kazaas and Gnutellas of this world. For example.. there is no search engine built in. A user doesn't search inside BitTorrent for your book to obtain it. She goes directly to your website and clicks the BitTorrent link that you have set up. Thus her client can guarentee that she gets exactly what you want to give her.
Of course, as you mention, there is still a stigma against peer-to-peer programs in general. This is probably because most of these programs are really designed to make it easy to illegally share copywrited work.
BitTorrent is different. It's designed from the ground up to solve the very problem that you are having. As people get more comfortable using it, I think the stigma will begin to fade.