I talked about it upthread, but this is a very, very long thread.

I think statutes and regulations are generally interpreted consistent with their purpose. And while I am not the DOT, I think I have some inkling of the purpose of their regulation. I can think of obvious ones:

1. To prevent airlines from canceling tickets as a result of what you might call "seller's remorse", after an intended fare reduction does not have the intended market effect or is determined to have cost the airline too much money, or engaging in similar forms of bad faith conduct with respect to non-mistaken airfares which in retrospect turned out to be dumb business decisions.

2. To protect people who go to an authorized agent of the airline, are quoted a very low fare, pay for a ticket, and go ahead and make travel plans, pay deposits, take time off of work, etc., only to have the airline come back to them and say "pay us thousands of dollars more or you won't fly!".

To prevent these things from happening, the DOT departed from the common law rule of unilateral mistake and said that instead, we would require airlines to honor mistaken fares to prevent against 1 and protect the people in category 2.

The question posed here is that you have a situation that doesn't really relate to either of the two purposes of the rule. United wasn't trial ballooning a ridculously low fare for their elite Global First product only for Danish people (and indeed, the EU regulation arguments made by people early in the thread basically refute that this could possibly be the case, as United wasn't even allowed to do this under EU law and therefore couldn't have been trying). And certainly for the most part, the people who bought these tickets are people whose local currency wasn't even the DKK and whose credit cards did not even actually have a Danish billing address. They clearly understood by their conduct that this was some sort of mistake, that if they booked in a different currency they would be quoted the "real" fare, and the error was discovered very, very fast, which means that a person would have had to have been acting unreasonably if they larded up on non-refundable travel deposits and reservations based on one of these tickets before UA notified them they weren't going to get to travel.

So the legal issue is, does the DOT regulation, which clearly applies where either of its purposes are being served, also apply in a situation where it is completely divorced from its purposes?

I suspect that the DOT will rule that it does not. Because it's entirely possible to protect people from airlines engaging in gamesmanship on their fares or people who innocently book a mistaken airfare and make their plans consistent with it while not applying the rule to a situation where the passengers had to consciously select a particular foreign currency and (perhaps) state an incorrect credit card billing address in order to get the mistake airfare, and did it precisely with the intention of obtaining an airfare that they knew was grossly erroneous.

But I do not say that with certainty. It is also possible-- and this is your best hope, I think-- that the DOT will decide that it is too big a can of worms to open up to start drawing distinctions between passengers who game the website and those who don't, and as a result will decide that the regulation extends to this case as well. (A third possibility is that this will be the straw that breaks the camel's back and the DOT will expedite publication of a rule repealing their regulation-- a result that I would consider very bad, because, as I said, I do think that the current regulation protects a class of travelers whom I think should be protected.)

What I will say with certainty is that I have no doubt that the DOT, and anyone in any capacity deciding any dispute based on these tickets, will at least give consideration to the manner in which they were booked and are certainly going to be aware of it. I realize people want to argue that the manner of booking is all irrelevant, but there's no way the DOT or anyone else is going to see this as exactly the same case as other mistake fares where no gaming of the website was necessary to claim the fare.