As the video link you posted demonstrates, you can freely resize the Picture in Picture by holding down the shift key while dragging the corner. However, the videographer there was working with a blur insert, so distortion was not a problem. If you freely resize an ordinary PiP photo there will be distortion because you are stretching or shrinking it out of its aspect ratio. But if you don't hold down the Shift key resizing the Picture in Picture will keep the same aspect ratio so there will be no distortion. However, then you would not be able to increase the width while keeping the height the same, as you have found. So it's a trade off -- a distorted free configuration versus an undistorted configuration that retains the original aspect ratio dimensions.
If, say, you wanted to make a picture wider but not higher, and avoid distortion, you would need to crop it before putting it into the Picture in Picture feature. You can do that by cropping the picture in the media browser screen that you get when you click on your project's name under the project media item in the upper left of the media sidebar. Select your photo in the media browser screen and then click on the crop tool icon (the one that looks like intersecting angles) in the tool bar at the top right of your screen. A little "Crop" square will appear to the left of the preview screen. Click on that. Then you can crop in the preview screen, using the adjustment rectangles that will allow to to freely crop in any dimensions that you want. Apply your changes by clicking on the blue Reset button in the upper right of your screen. Then drag the cropped photo into the timeline and insert it as a Picture in Picture. It will be distortion free, but of course some of the photo will be missing at the top and/or bottom where you cropped it.
-- Rich