I have been on Ebay for 8 years and being a 100% Ebayer have seen on occasion buyers threaten to leave negative feedback to get a discount or return an item. And after 8 years I was left negative feedback by a private feedback buyer. After a month of sending the item out he contacted me to state he hadn't received the item. I was on holiday at the time and asked for time to return home and get the proof of postage. I was then sent an immediate dispute to which I could resolve before getting home. I issued a refund immediately to the buyer and the dispute was closed.
I was then left negative feedback stating that I was unhelpful and took a month to give a refund. The day after the dispute was closed I received an email from Ebay thanking me for resolving the dispute so quickly! I have subsequently Googled the userid and the person in question has a track record of leaving negative feedback for sellers with 100% feedback. So even though his feedback is set to private, Google will reveal if a buyer has a history of being disruptive for the sake of it.
Remember, not all those with private feedback will pose problems, some like to keep history private for an assortment of reasons. As part of your listing include a request asking for private biddings to reveal their feedback before bidding and state if this is not met then their bid can be declined.
It's a disappointment that Ebay allow such buyers immunity. It is therefore down to us to tackle people who go to ruin professional sellers feedback without just cause until they bring in measures to prevent this.