I appreciate all the different views in this thread but allow me to explain my perspective, for better or worse. When an auction is bid up quickly by two parties, then the rest of the participants are often left to watch because the value quickly surpasses what they would be willing to bid. They never have the chance to get in on the auction at their best bid. But clearly, if the second place bidder is willing to honour their highest bid, then the issue of whether "anyone else would have bid" is moot.
Consider this scenario... an auction gets quickly bid up between PersonA and PersonB from $100 to $1000. PersonC watching from the sidelines would be willing to buy the domain for $250 but never gets a chance to place their bid because the bidding is so quick.
The auciton closes with PersonA winning at $1000. And later (possibly months) it is determined that PersonA is fraud. Maybe it has taken this long for a charge back to occur (charge backs can occur as long as 6 months to a year after a transaction occurs). So, if possible, the domain is taken back from the "winner".
Now, what many people in this thread say should happen is that the bids placed by PersonA should simply be declared void in which case PersonB would now get the domain for $100, the point at which the bidding war started.
But in fact, PersonC would argue they should have a chance to bid now that the war has cleared. However, if PersonB says their high bid stands, then the issue of PersonC's lower bid is moot.
So, awarding to PersonB without further competition is fair as long as the award is at their highest bid. Otherwise, the only fair thing to do is re-open the auction to all bidders excluding the original winner.
Ultimately, the second place bidder is being given a choice. They can say no, send the domain to a new auction, which is what we would do. We simply give the second place bidder the rights of first refusal before scheduling a re-auction. And if they choose to not buy the domain they now have the option to bid whatever they like in a new auction.
They also have the choice to say yes, I still value the domain at my high bid and rather than risk losing it in a re-auction, I'll take it.
But ultimately, the choice is theirs to make.