This seems like the "obvious" answer, at least in the timeless sense.

Maybe, but obvious answers to such problems are often wrong. Often, multiple different answers are each obviously the exclusively right answer. And look at all the people in this thread one-boxing. Not so obvious to them.

My reasoning was as stated, but I'm not going to use its "obviousness" as an additional argument in favour of it. And on reading the comments and the Facebook thread, I notice that I have neglected to consider the hypothetical situations in which the two numbers are different. On considering it, it seems that I should still argue as I did, using all the available information, i.e. that on this occasion the two numbers are the same. But it is merely obvious to me that this is so; I am not at all certain.

the obvious solution is unlikely to be fully correct, or else what would be the point of Eliezer posing the problem in the first place...

I'm disinclined to guess the right answer on the basis of predicting the hidden purposes of someone smarter than me. But I can, as it happens, think of a reason for posing a question whose "obvious" solution is completely right. It could be just the first of a garden path series of puzzles for which the "obvious" solutions are collectively inconsistent with any known decision theory.