Need to clarify...
the jpg can contain several "Tag Blocks"... EXIF, IPTC, XMP are the most common. Other applications save their own proprietry tags in their own defined tag blocks. Media Center is no different here, and saves its proprietry tags in an MJMD tag block.
When you ask MC to 'Remove Tags', it removes its own MJMD tag block, but leaves all the others alone.
There's a program out there called xnview mp, that lets you get selective regarding tag cleaning, offering options as per attached. "All other app markers" would include MC's MJMD tags.
Does that help?
-marko.