And still you don't give us any details...
Quick Find only checks local folders on your hard drive. Specifically, it checks the folder that you have set as the Cover Art location in Options->File Location->Cover Art (I screwed up in my last post and said it was under General), and the folder that the music actually resides in. Have you checked these two locations to see if there is any album art stored there that shouldn't be?
Why you would use Get From Internet (I would think would be obvious) is if you don't have cover art for an album or the art you have is low quality and you want to find out if some kind soul submitted higher quality art to YADB. You use Get From Internet and go through the list comparing what's available to what you have and choose which one you want to use. Unless you run Get From Internet and just click OK when it finishes its lookup (which would just accept the image with the highest number of votes from YADB - IMO a bad idea at the moment until the voting system has a chance to weed out the chaff and push the best stuff to the top), there's no way it's going to just automatically overwrite your local images.
The only place I can see where MC ever automatically downloads album art is in auto-import settings, where, from my experience, it seems to first check for art in the same folder as the music files and the Cover Art location. Only then does it appear to go online to get it. I could be wrong on this, though. I have that option unchecked.