This product is a great product.
However, by issuing the dialog box "UNC paths are not supported" in the browse window, you have communicated to the users the message that the entire product does not support UNC paths, which is untrue.
Clearly, since folks have been asking you for this feature for 10 years, it must not be a trivial feature to add.
How about this: Modify the message from "UNC paths are not supported" to "UNC paths are not supported in the browser. Consider drag-and-drop to Windows Explorer window.". This will communicate the scope of the issue, and a useful workaround.
It will also decrease the number of people asking for a feature that you have had on the "back burner" for a decade.
I needed to move files from a UNC path to a nfs path mounted on a linux server. I used the symlink solution, but that made this a pretty clumsy process. I ended up switching to FileZilla which supports UNC paths out of the box. I didn't know about dragging from an explorer window into winscp, but that is still a bit of a kludge.
Both apps support sftp, which is what we have enabled on linux, so ease of use wins it for filezila in my case.