This is what I found out:
1) Yes. After switching from Classic to Study Winamp grabs the studio-buttons instead of those scrollbars. I was able to reproduce it even with xml-files from Quinto. Same result.
2) But what worries me even more is the fact that your Study skin literally (!) can "damage" Classic Skin. How is this possible? I mean Classic is hardcoded within Winamp. I renamed the png files and was not able to switch to Classic.
But please look for yourself. On that screenshot you see Classic Skin (at least the context menu is from Classic) but the rest is from Study. Oh dear!
The scrollbars should be pink but are green - so again, the wrong png file is loaded. And the pink text color (and other pink graphics elements) is a sign that values are missing. Even switching to Modern Skin and Classic thereafter makes look Modern Skin just weird. Deleting the studio file is the only reliable help here.
Right now I could not say what causes this oddity, but if I were you I would abandon this project, grab the Original (=Modern Skin), tear it apart and make a fresh start from there. The idea of making "tutorial skins" is very noble but I would definitely want to rely on something that has been done a thousand times. And this would be Modern Skin.
Sorry I could not help you.