Here's another angle. Heard from more than one source that there was really no such thing as an official "PD". BMW apparently pulled standard g/s bikes off the production line and gave them the extra PD spec. There was no distinction from the frame numbers which bike was to be a g/s or a which bike a g/s PD.
The bikes with the genuinely signed tanks would undoubtedly have been "factory" models, but most tank signatures have long since eroded or tank been repainted/replaced. To add further complication, some UK (and probably also overseas) dealers did their own conversions to "PD" to enhance sales. Consequently, even bikes obtained with an original dealer sales invoice isn't guaranteed to be a "factory" model.
The distinction between g/s and PD wasn't particularly important at the time of original sale; you bought a PD if you preferred the look or needed a larger tank. Only since then have the PDs generated higher sales value disproportionate to the original cost of the extras. If your bike was made within the PD production time-frame then it might be a genuine PD, but then again, it might not.
That's how I've understood the situation to be for many years. It might be wrong but I'm just relating what I've heard from more than one source,