It's pretty unlikely you'll ever be able to create output clips that are the same size as the video clips you imported into your project.
I suppose you could open your original clip in a program like MediaInfo and look at its detailed specs and then try to create a custom output template that matched those specs exactly. But even then it's not likely your output will be a reflection of the size of the original file.
It's weird because I just tried doing the same thing in Photoshop and it exported the smaller clips perfectly. No messing around with any setting changes, just slice and render.
Photoshop is not Elements. They use different export settings.
Match Source means it takes on all properties such as height width etc from the project settings expect for the compression/codec used. That is set by the user.
When you are editing in Photoshop, you are editing the actual media file.
When you are editing in a video editor like Premiere Elements, you are adding the media file to a project and editing the project file.