There are definitely two or three different scenarios here. If I sell an item with some overlooked damage or stain, I would certainly prefer they did not try to clean it themselves or even take it to be cleaned without notifying me first. A spot might be removable with proper cleaning, but may set in permanently if done incorrectly. Most of the time I give the option to return it without cleaning or offer to help pay for repair or cleaning without a further option to return.
It would be hard to prove if a stain occurred after receipt or was already present upon sale unless of course it was in an obvious spot on the item which was shown clearly in the photos. If it was obviously a post sale stain, I wouldn't offer a refund or help with cleaning. That would be silly.
Also it's not that we sellers believe most buyers are scammers. It's just that eBay will side with the buyer 99% of the time whether the seller is at fault or not. I always try to give the buyer the benefit of the doubt, but sometimes you just have to draw a line somewhere. However drawing such a line will almost certainly end in a negative feedback. I know this, because I have 1. I drew the line and the buyer didn't like it, I didn't like the neg feedback either, but I had to stand for what was right regardless of the outcome.