Digital download hidden URL

We are creating a site that is purely for downloadable PDFs of out-of-print publications from our back-catalog. I've been testing ProductCart on an internal server before we replace our current solution from SmartCart (monthly fee and little site design flexibility, vs. ProductCart's total customizability and one-time fee).

For digital download product, SmartCart actually makes a copy of the PDF in another folder with a funky generated filename, and gives the customer the URL to that file. A cleanup process removes files from that folder that are past the "download link lifespan."

ProductCart is generating a unique URL for the order confirmation e-mail that the customer receives, but once they click on that link and the PDF opens in the browser, the browser's address bar shows the true original location of the PDF file. They could make a note of that and post it to some BBS, and everyone would have access to our product files.

Is there any way to make ProductCart truly hide and never reveal the URL of the download file? 

I know anyone out to steal is going to. Just one of those things to keep the honest people honest, and make anyone who wants to share the file have to go to the effort of uploading it elsewhere, rather than conveniently passing the URL along.