The Asirra paper isn't from a ML research group. The statement: "Barring a major advance in machine vision, we expect computers will have no better than a 1/54,000 chance of solving it" is just a statement of fact - it wasn't any forms of prediction.

If you read the paper you note that they surveyed researchers about the current state of the art ("Based on a survey of machine vision literature and vision ex- perts at Microsoft Research, we believe classification accuracy of better than 60% will be difficult without a significant advance in the state of the art.") and noted what had been achieved as PASCAL 2006 ("The 2006 PASCAL Visual Object Classes Challenge [4] included a competition to identify photos as containing several classes of objects, two of which were Cat and Dog. Although cats and dogs were easily distinguishable from other classes (e.g., “bicycle”), they were frequently confused with each other.)

I was working in an adjacent field at the time. I think the general feeling was that advances in image recognition were certainly possible, but no one knew how to get above the 90% accuracy level reliably. This was in the day of hand coded (and patented!) feature extractors.

OTOH, stock market prediction via learning methods has a long history, and plenty of reasons to think that long term prediction is actually impossible. Unlike vision systems there isn't another thing that we can point to to say that "it must be possible" and in this case we are literally trying to predict the future.

Short term prediction works well in some cases in a statistical sense, but long term isn't something that new technology seems likely to solve.