For now I am assuming that your Premiere Elements 12 is on Windows 7, 8, or 8.1 64 bit.
What specific PiP effect did you use....was it from fxEffects/Presets and one of the 25% or 40% ones or did you create the picture in picture effect by scaling down an image over the background below it?
I suspect that you have a project mismatch of settings somewhere along the line, so prepare yourself for the following questions.besides the details of how you created the PiP effect.
1. What are the properties of your source media - brand/model/settings for camera that recorded the files
Interlaced or Progressive
Pixel Aspect Ratio
2. When you played back the Timeline content in the Edit area monitor, did the monitor space have any black borders?
3. What are the details of your export...
Publish+Share/what/what and what preset? Did you use the defaults for the preset selected or did you customize the preset
under the Advanced Button/Video Tab of that preset?
Let us start here, and then we can decided what next based on your details.