It would be very easy to turn this debate around to one of ‘best practice’ by suggesting that if you’re uploading another version of the PDF, then the name of that PDF should be different, most likely by incorporating a version number or date.
We have a few clients in a very similar situation. Once a PDF has been downloaded, there’s then a static copy of something floating around which can be distributed by some other means (e.g. email). It’s therefore important that this PDF is versioned, by date/number so that you know which version you have and whether it’s current.
To assist content editors, a single 301 redirect is maintained to point to the current/latest version of the uniquely named PDF. The PDF is linked to the ‘static’ link (which is redirected) in content so the editor’s job is to upload the new PDF, then amend the redirect to point to the new upload.
I don’t accept the “people are too busy to do something properly” argument. I find it better to help editors understand why it’s sometimes better to spend 10 more seconds doing something rather than the way they find quickest.