I said that if a person on the BB accepted my fixed price, he would then go to the ebay action and overbid. At this point, with the Bulletin Board bidder as the high bidder, I would then stop the auction prematurely and sell to the high bidder, who happens to be the BB bidder.

Example. I have a chip on ebay. The current high bid is $5 with 7 days left. I agree to sell for $50 to Dave Smith from Greg's bb. Dave then goes to my ebay auction and overbids. Let's say cuurent bid becomes $15 with Dave Smith as high bidder. I then stop the auction and sell to Dave for $50.

The only problem is if the $5 bidder had a proxy bid of $50 or more, then you are right. The high eBay bidder gets it.