But there is a workaround (which sounds more complicated than it really is!)
Highlight the edited clip and Edit --> Copy (or Control-C)
Open a new project (make sure you save the original project first).
Edit --> Paste (or Control-V) to paste the edited clip onto the timeline of the new project. That is the only thing that will be on the timeline.
Go to Produce and create a file - avi or mpeg.
Close the second project - no need to save it as all you want is the produced file.
Go back to your original project and import the file you just created, and copy it to your PIP track.
Hope that helps.
Robert