I would always think that if MP3tag shows the modified data correctly, then MP3tag has done its duty.
If the player then acts up, it would be a question for the support of the player why the player does not behave.
Anyway: it could be that there are still folder.jpg files lurking around in the file folder.
Or that the windows media player cache still holds the old picture.
In both cases only deleting the old data will help, if this is the cause.
The WMP cache resides in
%localappdata%\Microsoft\Media Player\Grafikcache\LocalMLS
That folder can be removed without any further side effects.