You would get questions like 'Why was my bid not recorded when it was valid' Or 'Why was the selling price so high. You can't understand the selling price if the next to highest bid isn't displayed. I think the bid history should stay as it is, record and display all valid bids, and reject the rest. In Shirleys example if only one of the three bids were displayed, the winner would wonder why the selling price was over $12 instead of $10.
Another way that might work is to record ALL bids, and flag (maybe with a different color) the invalid bids as being 'to low', or 'increment not met'. I think that 'might' make it less confusing.
The only other option is to change all bid increments to one cent. Each higher bid is valid, and the highest bidder always wins. I imagine eBay doesn't do this to keep the number of bids down. An auction could have bid counts numbering in the hundreds or more, as each bidder raises the price by 3-4 cents at a time.
