I've also wondered about this argument, though I didn't know it had a name. I thought of it when I heard it mentioned that it is "natural" for the Sun to be about halfway through its main-sequence lifetime, since it would be unlikely to be very near the beginning or very near the end. I don't know the relative merits of the two different applications of this general idea, but I would agree that Madalone's argument completely shatters the Carter catastrophe idea. (Fram's point is also well taken, but there is already nothing left of the argument that survives the OP!). It's a little like asking someone who wins a grand prize in a lottery what they would estimate their chances of winning were. It would boggle their mind if they hadn't really thought about it before. Yet somebody had to win, and that person is in such a special position that you can't ask them to apply the same logic as a "normal" person.

That's in essence what Madalone has said, and has shown that the Carter catastrophe hypothesis has already been disproven. The only thing I would add is that this is an example of the subtleties presented by the anthropic principle-- you can't ask the people who are in a special place to use probability arguments that assume they are not in a special place. Otherwise, why could I not turn the catastrophe argument around, and conclude that humans will survive for a significant fraction of the duration of the universe, otherwise if "today" is a date chosen at random, what would have been the likelihood that humans would be here today?