Do you have links to your site embedded in those PDF files?

No, the PDFs were produced by the manufacturers

Crazy! How could they be shown as linking to your site when they host the manufacturer's PDF on their servers and link to it?

Why should google consider you as the source for the PDF when it is one from the manufacturer?

They probably linked to the PDF on your site and then decided to steal it it and host it on theirs.But google might have seen those links to the PDF on your server in the past.

What is the discovery date for the links? You should not consider the discovery date on the main page of the WMT report.But when you click through the link on the main report, you will find all links to that page and their discovery dates. what are those dates?

As these files are duplicates, it would make sense from G's point of view to add the strength of any links to the duplicates to (what in their opinion is) the original file.
It's not a stretch of the imagination to assume that G thinks you're the original creator of the PDFs.
Do you have a stronger site than the manufacturer, or are one of the first sites to host the files? Does the manufacturer make the files publicly available, or link to them deeper in the site compared to you?

It's not a stretch of the imagination to assume that G thinks you're the original creator of the PDFs.

that would make my link building tasks a whole lot easier.

A mistake on G's part, however, isn't exactly a sustainable link building strategy, and I'm sure you'd think very differently if (when?) you're on the other side of the fence and your links count towards the manufacturer's site.
I know that many people on this site can't wait for G to pick up on their site as the original...
To help us all, can you please let us know:

Do you have a stronger site than the manufacturer, or are one of the first sites to host the files? Does the manufacturer make the files publicly available, or link to them deeper in the site compared to you?

Does your site have sitelink status when you search for its name or its primary keywords ?

I'm wondering if a mere mention of those words, in the proper context, results in Google assigning a virtual link between documents, pdf or not. Normally we wouldn't be shown such "virtual" connections but since it's a pdf perhaps the filter missed the page and reported it?

Only Google knows.

Makes me wonder whether this is just a reporting glitch in WMT or an actual bug in Google's backlink attribution code itself, something that actually could affect ranking.

Our site does have site links when searched for by our brand and we rank higher than the manufacturer for most products. Our product pages that link to the PDFs tend to be closer to the home page than the manufacturers.

If I had created the PDFs and others had copied and hosted them is this the same thing I would see?

I also rank higher than the manufacturer for the PDFs so maybe G does think I'm the creator. It's bizarre though as many of the files were around for 6 months or more before I added them.